Minuscule 630: Difference between revisions

Revision as of 22:47, 25 May 2013

The circle-based 1.1-skeleton (heavy dark edges) and 0.9-skeleton (light dashed blue edges) of a set of 100 random points in a square.

In computational geometry and geometric graph theory, a β-skeleton or beta skeleton is an undirected graph defined from a set of points in the Euclidean plane. Two points p and q are connected by an edge whenever all the angles prq are sharper than a threshold determined from the numerical parameter β.

Circle-based definition

Let β be a positive real number, and calculate an angle θ using the formulas

\theta ={\begin{cases}\sin ^{-1}{\frac {1}{\beta }},&{\text{if }}\beta \geq 1\\\pi -\sin ^{-1}{\beta },&{\text{if }}\beta \leq 1\end{cases}}

For any two points p and q in the plane, let R_pq be the set of points for which angle prq is greater than θ. Then R_pq takes the form of a union of two open disks with diameter βd(p,q) for β ≥ 1 and θ ≤ π/2, and it takes the form of the intersection of two open disks with diameter d(p,q)/β for β ≤ 1 and θ ≥ π/2. When β = 1 the two formulas give the same value θ = π/2, and R_pq takes the form of a single open disk with pq as its diameter.

The β-skeleton of a discrete set S of points in the plane is the undirected graph that connects two points p and q with an edge pq whenever R_pq contains no points of S. That is, the β-skeleton is the empty region graph defined by the regions R_pq.^[1] When S contains a point r for which angle prq is greater than θ, then pq is not an edge of the β-skeleton; the β-skeleton consists of those pairs pq for which no such point r exists.

Lune-based definition

Some authors use an alternative definition in which the empty regions R_pq for β > 1 are not unions of two disks but rather lenses (more often called in this context "lunes"), intersections of two congruent disks with diameter βd(pq), such that line segment pq lies on a radius of both disks and such that the points p and q both lie on the boundary of the intersection. As with the circle-based β-skeleton, the lune-based β-skeleton has an edge pq whenever region R_pq is empty of other input points. For this alternative definition, the relative neighborhood graph is a special case of a β-skeleton with β = 2. The two definitions coincide for β ≤ 1, and for larger values of β the circle-based skeleton is a subgraph of the lune-based skeleton.

One important difference between the circle-based and lune-based β-skeletons is that, for any point set that does not lie on a single line, there always exists a sufficiently large value of β such that the circle-based β-skeleton is the empty graph. In contrast, if a pair of points p and q has the property that, for all other points r, one of the two angles pqr and qpr is obtuse, then the lune-based β-skeleton will contain edge pq no matter how large β is.

History

β-skeletons were first defined by Template:Harvtxt as a scale-invariant variation of the alpha shapes of Template:Harvtxt. The name, "β-skeleton", reflects the fact that in some sense the β-skeleton describes the shape of a set of points in the same way that a topological skeleton describes the shape of a two-dimensional region. Several generalizations of the β-skeleton to graphs defined by other empty regions have also been considered.^[1]^[2]

Properties

If β varies continuously from 0 to ∞, the circle-based β-skeletons form a sequence of graphs extending from the complete graph to the empty graph. The special case β = 1 leads to the Gabriel graph, which is known to contain the Euclidean minimum spanning tree; therefore, the β-skeleton also contains the Gabriel graph and the minimum spanning tree whenever β ≤ 1.

For any constant β, a fractal construction resembling a flattened version of the Koch snowflake can be used to define a sequence of point sets whose β-skeletons are paths of arbitrarily large length within a unit square. Therefore, unlike the closely related Delaunay triangulation, β-skeletons are not geometric spanners.^[3]

Algorithms

A naïve algorithm that tests each triple p, q, and r for membership of r in the region R_pq can construct the β-skeleton of any set of n points in time O(n³).

When β ≥ 1, the β-skeleton (with either definition) is a subgraph of the Gabriel graph, which is a subgraph of the Delaunay triangulation. If pq is an edge of the Delaunay triangulation that is not an edge of the β-skeleton, then a point r that forms a large angle prq can be found as one of the at most two points forming a triangle with p and q in the Delaunay triangulation. Therefore, for these values of β, the circle-based β-skeleton for a set of n points can be constructed in time O(n log n) by computing the Delaunay triangulation and using this test to filter its edges.^[2]

For β < 1, a different algorithm of Template:Harvtxt allows the construction of the β-skeleton in time O(n²). No better worst-case time bound is possible because, for any fixed value of β smaller than one, there exist point sets in general position (small perturbations of a regular polygon) for which the β-skeleton is a complete graph with a quadratic number of edges. In the same quadratic time bound, the entire β-spectrum (the sequence of circle-based β-skeletons formed by varying β) may also be calculated.

Applications

The circle-based β-skeleton may be used in image analysis to reconstruct the shape of a two-dimensional object, given a set of sample points on the boundary of the object (a computational form of the connect the dots puzzle where the sequence in which the dots are to be connected must be deduced by an algorithm rather than being given as part of the puzzle). Although, in general, this requires a choice of the value of the parameter β, it is possible to prove that the choice β = 1.7 will correctly reconstruct the entire boundary of any smooth surface, and not generate any edges that do not belong to the boundary, as long as the samples are generated sufficiently densely relative to the local curvature of the surface.^[4] However in experimental testing a lower value, β = 1.2, was more effective for reconstructing street maps from sets of points marking the center lines of streets in a geographic information system.^[5] For generalizations of the β-skeleton technique to reconstruction of surfaces in three dimensions, see Template:Harvtxt.

Circle-based β-skeletons have been used to find subgraphs of the minimum weight triangulation of a point set: for sufficiently large values of β, every β-skeleton edge can be guaranteed to belong to the minimum weight triangulation. If the edges found in this way form a connected graph on all of the input points, then the remaining minimum weight triangulation edges may be found in polynomial time by dynamic programming. However, in general the minimum weight triangulation problem is NP-hard, and the subset of its edges found in this way may not be connected.^[6]

β-skeletons have also been applied in machine learning to solve geometric classification problems^[7] and in wireless ad hoc networks as a mechanism for controlling communication complexity by choosing a subset of the pairs of wireless stations that can communicate with each other.^[8]

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

Template:Refbegin

Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

Template:Refend

[ccl-1] 1.0 ^1.1 Template:Harvtxt.

[v-2] 2.0 ^2.1 Template:Harvtxt.

[3] Template:Harvtxt; Template:Harvtxt; Template:Harvtxt.

[4] Template:Harvtxt; Template:Harvtxt.

[5] Template:Harvtxt.

[6] Template:Harvtxt; Template:Harvtxt.

[7] Template:Harvtxt; Template:Harvtxt.

[8] Template:Harvtxt.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

Minuscule 630: Difference between revisions

Revision as of 22:47, 25 May 2013

Contents

Circle-based definition

Lune-based definition

History

Properties

Algorithms

Applications

Notes

References

Navigation menu

@@ Line 1: / Line 1: @@
+[[File:Beta-skeleton.svg|thumb|300px|The circle-based 1.1-skeleton (heavy dark edges) and 0.9-skeleton (light dashed blue edges) of a set of 100 random points in a square.]]
+In [[computational geometry]] and [[geometric graph theory]], a '''''β''-skeleton''' or '''beta skeleton''' is an [[undirected graph]] defined from a set of points in the [[Euclidean plane]]. Two points ''p'' and ''q'' are connected by an edge whenever all the angles ''prq'' are sharper than a threshold determined from the numerical parameter&nbsp;''β''.
+==Circle-based definition==
+[[File:Beta-skeleton regions.svg|thumb|The empty regions ''R''<sub>''pq''</sub> defining the circle-based ''β''-skeleton. Left: ''β''&nbsp;<&nbsp;1. Center: ''β''&nbsp;=&nbsp;1. Right: ''β''&nbsp;>&nbsp;1.]]
+Let ''β'' be a positive [[real number]], and calculate an angle ''θ'' using the formulas
-Visit our essay writing company and enjoy quality services. While selecting the company students should not make price packages their priority. Whenever students are assigned to write high school vs. A photographic essay is an attempt to cover a topic with a linked series of photographs; it may or may not have an. If the essay contains any facts, check their accuracy with reliable sources. <br><br>Definition essay- A definition essay defines a particular term. This will make your life much easier, and your teacher or professor will love you for not having to strain to read what you attempted to squeeze between lines in illegible scribble. Usually do not stress since we'll do anything for you personally. However, the fact is completely different from this myth, which is writing a research paper thesis is not at all an easy business; rather it is a crucial activity because it requires time and effort to come up with proficient answers and explanation to queries, best suiting to the sense of question. Our experts also impart variety of services like Custom Essay Writing, Critical Essay Writing, Essay Project Help, Essay writing Help. <br><br>Before writing, identify all parts of the prompt, and jot down some ideas for how to answer each element in your response. com will provide a very good opportunity for college students to get involved in a greater capacity in writing their essays. provide persuasive essay tips to students in all academic levels. Clients are assured to get all writing services regardless of their geographical locations since nowadays internet can be accessible in any corners of the planet as long as there is an internet connection within the client’s locale. We highly value to satisfaction of our clients in need of our freelance essay writing services. <br><br>What makes the argument that 'essay writing is an art' hold water, however, is the fact that a considerable number of those who struggle with the writing essay task are not necessarily daft people in general terms, but rather people who simply happen to lack aptitude in the fine art that is essay writing. Such reliable companies employ professionally qualified and experienced essay writers in their respective fields of specialization.  If you cherished this write-up and you would like to get a lot more data with regards to [http://site1.plumbingnumbers.com/explaining-straightforward-secrets-essay-writing buy narrative essay] kindly stop by our own site. Keep a tab on your sources of information so you can access it later. And they can ask the kinds of quirky questions'both short answer and full-on essays'that require an element of self-reflection on the part of the applicant. In order to strongly support the viewpoint you hold about the topic, this argument should be the most convincing piece of evidence. <br><br>- Essays that make every effort to portray the writer as "perfect" and just try too hard. The company has employed professional company writers who are trained on how to write academic documents in all academic areas. In essay writing, getting failing grades is the main fear of students but it is just an instigator of other apprehensions - as the writing process progresses, the main concern branches out to more precise fears. "Knowing the truth" behind your recently rejected work will not help. Most of online essay writing companies are there t make money and thus students should be keen when seeking their analytical essay writing help.
+:<math>\theta = \begin{cases} \sin^{-1} \frac{1}{\beta}, & \text{if }\beta \ge 1 \\ \pi - \sin^{-1}{\beta}, & \text{if }\beta\le 1\end{cases}</math>
+For any two points ''p'' and ''q'' in the plane, let ''R''<sub>''pq''</sub> be the set of points for which angle ''prq'' is greater than&nbsp;''θ''. Then ''R''<sub>''pq''</sub> takes the form of a union of two open disks with diameter ''βd''(''p'',''q'') for ''β''&nbsp;≥&nbsp;1 and ''θ''&nbsp;≤&nbsp;π/2, and it takes the form of the intersection of two open disks with diameter ''d''(''p'',''q'')/''β'' for ''β''&nbsp;≤&nbsp;1 and ''θ''&nbsp;≥&nbsp;π/2. When ''β''&nbsp;=&nbsp;1 the two formulas give the same value ''θ''&nbsp;=&nbsp;π/2, and ''R''<sub>''pq''</sub> takes the form of a single open disk with ''pq'' as its diameter.
+The ''β''-skeleton of a [[Isolated point|discrete set]] ''S'' of points in the plane is the [[undirected graph]] that connects two points ''p'' and ''q'' with an edge ''pq'' whenever ''R''<sub>''pq''</sub> contains no points of ''S''. That is, the ''β''-skeleton is the empty region graph defined by the regions ''R''<sub>''pq''</sub>.<ref name="ccl">{{harvtxt|Cardinal|Collette|Langerman|2009}}.</ref> When ''S'' contains a point ''r'' for which angle ''prq'' is greater than ''θ'', then ''pq'' is not an edge of the ''β''-skeleton; the ''β''-skeleton consists of those pairs ''pq'' for which no such point ''r'' exists.
+==Lune-based definition==
+Some authors use an alternative definition in which the empty regions ''R''<sub>''pq''</sub> for ''β''&nbsp;>&nbsp;1 are not unions of two disks but rather [[Lens (geometry)|lenses]] (more often called in this context "[[Lune (mathematics)|lunes]]"), intersections of two congruent disks with diameter ''βd''(''pq''), such that line segment ''pq'' lies on a radius of both disks and such that the points ''p'' and ''q'' both lie on the boundary of the intersection. As with the circle-based ''β''-skeleton, the lune-based ''β''-skeleton has an edge ''pq'' whenever region ''R''<sub>''pq''</sub> is empty of other input points. For this alternative definition, the [[relative neighborhood graph]] is a special case of a ''β''-skeleton with ''β''&nbsp;=&nbsp;2. The two definitions coincide for ''β''&nbsp;≤&nbsp;1, and for larger values of ''β'' the circle-based skeleton is a [[Glossary of graph theory#Subgraphs|subgraph]] of the lune-based skeleton.
+One important difference between the circle-based and lune-based ''β''-skeletons is that, for any point set that does not lie on a single line, there always exists a sufficiently large value of ''β'' such that the circle-based ''β''-skeleton is the [[empty graph]]. In contrast, if a pair of points ''p'' and ''q'' has the property that, for all other points ''r'', one of the two angles ''pqr'' and ''qpr'' is obtuse, then the lune-based ''β''-skeleton will contain edge ''pq'' no matter how large ''β'' is.
+==History==
+''β''-skeletons were first defined by {{harvtxt|Kirkpatrick|Radke|1985}} as a [[Scale invariance|scale-invariant]] variation of the [[alpha shape]]s of {{harvtxt|Edelsbrunner|Kirkpatrick|Seidel|1983}}. The name, "''β''-skeleton", reflects the fact that in some sense the ''β''-skeleton describes the shape of a set of points in the same way that a [[topological skeleton]] describes the shape of a two-dimensional region. Several generalizations of the ''β''-skeleton to graphs defined by other empty regions have also been considered.<ref name="ccl"/><ref name="v"/>
+==Properties==
+If ''β'' varies continuously from 0 to ∞, the circle-based ''β''-skeletons form a sequence of graphs extending from the [[complete graph]] to the [[empty graph]]. The special case ''β''&nbsp;=&nbsp;1 leads to the [[Gabriel graph]], which is known to contain the [[Euclidean minimum spanning tree]]; therefore, the ''β''-skeleton also contains the Gabriel graph and the minimum spanning tree whenever ''β''&nbsp;≤&nbsp;1.
+For any constant ''β'', a [[fractal]] construction resembling a flattened version of the [[Koch snowflake]] can be used to define a sequence of point sets whose ''β''-skeletons are paths of arbitrarily large length within a unit square. Therefore, unlike the closely related [[Delaunay triangulation]], ''β''-skeletons are not [[geometric spanner]]s.<ref>{{harvtxt|Eppstein|2002}}; {{harvtxt|Bose|Devroye|Evans|Kirkpatrick|2002}}; {{harvtxt|Wang|Li|Moaveninejad|Wang|2003}}.</ref>
+==Algorithms==
+A [[naïve algorithm]] that tests each triple ''p'', ''q'', and ''r'' for membership of ''r'' in the region ''R''<sub>''pq''</sub> can construct the ''β''-skeleton of any set of ''n'' points in time O(''n''<sup>3</sup>).
+When ''β''&nbsp;≥&nbsp;1, the ''β''-skeleton (with either definition) is a subgraph of the Gabriel graph, which is a subgraph of the [[Delaunay triangulation]]. If ''pq'' is an edge of the Delaunay triangulation that is not an edge of the ''β''-skeleton, then a point ''r'' that forms a large angle ''prq'' can be found as one of the at most two points forming a triangle with ''p'' and ''q'' in the Delaunay triangulation. Therefore, for these values of ''β'', the circle-based ''β''-skeleton for a set of ''n'' points can be constructed in time O(''n''&nbsp;log&nbsp;''n'') by computing the Delaunay triangulation and using this test to filter its edges.<ref name="v">{{harvtxt|Veltkamp|1992}}.</ref>
+For ''β''&nbsp;<&nbsp;1, a different algorithm of {{harvtxt|Hurtado|Liotta|Meijer|2003}} allows the construction of the ''β''-skeleton in time O(''n''<sup>2</sup>). No better worst-case time bound is possible because, for any fixed value of ''β'' smaller than one, there exist point sets in general position (small perturbations of a [[regular polygon]]) for which the ''β''-skeleton is a [[complete graph]] with a quadratic number of edges. In the same quadratic time bound, the entire ''β''-spectrum (the sequence of circle-based ''β''-skeletons formed by varying ''β'') may also be calculated.
+==Applications==
+The circle-based ''β''-skeleton may be used in [[image analysis]] to reconstruct the shape of a two-dimensional object, given a set of sample points on the boundary of the object (a computational form of the [[connect the dots]] puzzle where the sequence in which the dots are to be connected must be deduced by an algorithm rather than being given as part of the puzzle). Although, in general, this requires a choice of the value of the parameter ''β'', it is possible to prove that the choice ''β''&nbsp;=&nbsp;1.7 will correctly reconstruct the entire boundary of any smooth surface, and not generate any edges that do not belong to the boundary, as long as the samples are generated sufficiently densely relative to the local [[curvature]] of the surface.<ref>{{harvtxt|Amenta|Bern|Eppstein|1998}}; {{harvtxt|O'Rourke|2000}}.</ref> However in experimental testing a lower value, ''β''&nbsp;=&nbsp;1.2, was more effective for reconstructing street maps from sets of points marking the center lines of streets in a [[geographic information system]].<ref>{{harvtxt|Radke|Flodmark|1999}}.</ref> For generalizations of the ''β''-skeleton technique to reconstruction of surfaces in three dimensions, see {{harvtxt|Hiyoshi|2007}}.
+Circle-based ''β''-skeletons have been used to find subgraphs of the [[minimum weight triangulation]] of a point set: for sufficiently large values of ''β'', every ''β''-skeleton edge can be guaranteed to belong to the minimum weight triangulation. If the edges found in this way form a [[connected graph]] on all of the input points, then the remaining minimum weight triangulation edges may be found in [[polynomial time]] by [[dynamic programming]]. However, in general the minimum weight triangulation problem is NP-hard, and the subset of its edges found in this way may not be connected.<ref>{{harvtxt|Keil|1994}}; {{harvtxt|Cheng|Xu|2001}}.</ref>
+''β''-skeletons have also been applied in [[machine learning]] to solve geometric [[Statistical classification|classification]] problems<ref>{{harvtxt|Zhang|King|2002}}; {{harvtxt|Toussaint|2005}}.</ref> and in [[wireless ad hoc network]]s as a mechanism for controlling communication complexity by choosing a subset of the pairs of wireless stations that can communicate with each other.<ref>{{harvtxt|Bhardwaj|Misra|Xue|2005}}.</ref>
+==Notes==
+{{reflist|2}}
+==References==
+{{refbegin|2}}
+*{{citation
+ | last1 = Amenta | first1 = Nina
+ | last2 = Bern | first2 = Marshall
+ | last3 = Eppstein | first3 = David | author3-link = David Eppstein
+ | issue = 2
+ | journal = Graphical Models & Image Processing
+ | pages = 125–135
+ | title = The crust and the beta-skeleton: combinatorial curve reconstruction
+ | url = http://www.cs.utexas.edu/users/amenta/pubs/crust.ps.gz
+ | volume = 60/2
+ | year = 1998}}.
+*{{citation
+  | last1 = Bhardwaj | first1 = Manvendu
+ | last2 = Misra | first2 = Satyajayant
+ | last3 = Xue | first3 = Guoliang
+ | contribution = Distributed topology control in wireless ad hoc networks using ß-skeleton
+ | title = Workshop on High Performance Switching and Routing (HPSR 2005), Hong Kong, China
+ | url = http://www.public.asu.edu/~ssatyaja/papers/hpsr05.pdf}}.
+*{{citation
+ | last1 = Bose | first1 = Prosenjit
+ | last2 = Devroye | first2 = Luc
+ | last3 = Evans | first3 = William
+ | last4 = Kirkpatrick | first4 = David G. | author4-link = David G. Kirkpatrick
+ | contribution = On the spanning ratio of Gabriel graphs and ''β''-skeletons
+ | doi = 10.1007/3-540-45995-2_42
+ | pages = 77–97
+ | publisher = Springer-Verlag
+ | series = Lecture Notes in Computer Science
+ | title = LATIN 2002: Theoretical Informatics
+ | volume = 2286
+ | year = 2002}}.
+*{{citation
+ | last1 = Cardinal | first1 = Jean
+ | last2 = Collette | first2 = Sébastian
+ | last3 = Langerman | first3 = Stefan
+ | doi = 10.1016/j.comgeo.2008.09.003
+ | issue = 3
+ | journal = Computational Geometry Theory & Applications
+ | pages = 183–195
+ | title = Empty region graphs
+ | volume = 42
+ | year = 2009}}.
+*{{citation
+ | last1 = Cheng | first1 = Siu-Wing
+ | last2 = Xu | first2 = Yin-Feng
+ | doi = 10.1016/S0304-3975(00)00318-2
+ | issue = 1–2
+ | journal = Theoretical Computer Science
+ | pages = 459–471
+ | title = On ''β''-skeleton as a subgraph of the minimum weight triangulation
+ | volume = 262
+ | year = 2001}}.
+*{{citation
+ | last1 = Edelsbrunner | first1 = Herbert | author1-link = Herbert Edelsbrunner
+ | last2 = Kirkpatrick | first2 = David G. | author2-link = David G. Kirkpatrick
+ | last3 = Seidel | first3 = Raimund | author3-link = Raimund Seidel
+ | doi = 10.1109/TIT.1983.1056714
+ | issue = 4
+ | journal = IEEE Transactions on Information Theory
+ | pages = 551–559
+ | title = On the shape of a set of points in the plane
+ | volume = 29
+ | year = 1983}}.
+*{{citation
+ | last = Eppstein | first = David | author-link = David Eppstein
+ | doi = 10.1016/S0925-7721(01)00055-4
+ | issue = 1
+ | journal = Computational Geometry Theory & Applications
+ | pages = 43–52
+ | title = Beta-skeletons have unbounded dilation
+ | volume = 23
+ | year = 2002
+ | arxiv = cs.CG/9907031}}.
+*{{citation
+ | last = Hiyoshi | first = H.
+ | contribution = Greedy beta-skeleton in three dimensions
+ | doi = 10.1109/ISVD.2007.27
+ | pages = 101–109
+ | title = Proc. 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)
+ | year = 2007}}.
+*{{citation
+ | last1 = Hurtado | first1 = Ferran
+ | last2 = Liotta | first2 = Giuseppe
+ | last3 = Meijer | first3 = Henk
+ | doi = 10.1016/S0925-7721(02)00129-3
+ | issue = 1–2
+ | journal = Computational Geometry Theory & Applications
+ | pages = 35–49
+ | title = Optimal and suboptimal robust algorithms for proximity graphs
+ | volume = 25
+ | year = 2003}}.
+*{{citation
+ | last = Keil | first = J. Mark
+ | doi = 10.1016/0925-7721(94)90014-0
+ | issue = 1
+ | journal = Computational Geometry Theory & Applications
+ | pages = 18–26
+ | title = Computing a subgraph of the minimum weight triangulation
+ | url = http://www.cs.ust.hk/mjg_lib/Library/Keil94.pdf
+ | volume = 4
+ | year = 1994}}.
+*{{citation
+ | last1 = Kirkpatrick | first1 = David G. | author1-link = David G. Kirkpatrick
+ | last2 = Radke | first2 = John D.
+ | contribution = A framework for computational morphology
+ | location = Amsterdam
+ | pages = 217–248
+ | publisher = North-Holland
+ | series = Machine Intelligence and Pattern Recognition
+ | title = Computational Geometry
+ | volume = 2
+ | year = 1985}}.
+*{{citation
+ | last = O'Rourke | first = Joseph | author-link = Joseph O'Rourke (professor)
+ | doi = 10.1145/346048.346050
+ | issue = 1
+ | journal = [[SIGACT News]]
+ | pages = 28–30
+ | title = Computational Geometry Column 38
+ | volume = 31
+ | year = 2000
+ | arxiv = cs.CG/0001025}}.
+*{{citation
+ | last1 = Radke | first1 = John D.
+ | last2 = Flodmark | first2 = Anders
+ | issue = 1
+ | journal = Geographic Information Sciences
+ | pages = 15–23
+ | title = The use of spatial decompositions for constructing street centerlines
+ | url = http://www.iseis.cuhk.edu.hk/downloads/full_paper/1999-15-23.pdf
+ | volume = 5
+ | year = 1999}}.
+*{{citation
+ | last = Toussaint | first = Godfried | author-link = Godfried Toussaint
+ | doi = 10.1142/S0218195905001622
+ | issue = 2
+ | journal = International Journal of Computational Geometry and Applications
+ | pages = 101–150
+ | title = Geometric proximity graphs for improving nearest neighbor methods in instance-based learning and data mining
+ | volume = 15
+ | year = 2005}}.
+*{{citation
+ | last = Veltkamp | first = Remko C.
+ | doi = 10.1016/0925-7721(92)90003-B
+ | issue = 4
+ | journal = Computational Geometry Theory & Applications
+ | pages = 227–246
+ | title = The γ-neighborhood graph
+ | url = http://www.cs.uu.nl/groups/MG/multimedia/publications/art/cgta1992.pdf
+ | volume = 1
+ | year = 1992}}.
+*{{citation
+ | last1 = Wang | first1 = Weizhao
+ | last2 = Li | first2 = Xiang-Yang
+ | last3 = Moaveninejad | first3 = Kousha
+ | last4 = Wang | first4 = Yu
+ | last5 = Song | first5 = Wen-Zhan
+ | contribution = The spanning ratio of ''β''-skeletons
+ | pages = 35–38
+ | title = Proc. 15th Canadian Conference on Computational Geometry (CCCG 2003)
+ | url = http://www.cccg.ca/proceedings/2003/7.pdf
+ | year = 2003}}.
+*{{citation
+ | last1 = Zhang | first1 = Wan
+ | last2 = King | first2 = Irwin
+ | contribution = Locating support vectors via ''β''-skeleton technique
+ | pages = 1423–1427
+ | title = Proc. Proceedings of the 9th International Conference on Neural Information Processing (ICONIP'02), Orchid Country Club, Singapore, November 18-22, 2002
+ | url = http://www.cs.cuhk.hk/~king/PUB/ICONIP2002-cr1968.pdf
+ | year = 2002}}.
+{{refend}}
+[[Category:Euclidean plane geometry]]
+[[Category:Geometric graphs]]
+[[Category:Computational geometry]]

Minuscule 630: Difference between revisions

Revision as of 22:47, 25 May 2013

Circle-based definition

Lune-based definition

History

Properties

Algorithms

Applications

Notes

References

Navigation menu

Search