Coulomb's constant: Difference between revisions

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In [[graph theory]], a '''connected dominated set''' and a '''maximum leaf spanning tree''' are two closely related structures defined on an [[undirected graph]].
CCS has obtained feedback that the business community has faced sharp will increase in industrial property costs and rentals in recent years. The concerns were that these increases had been attributable to the growing presence of REITs in the [http://www.healthymonadnock.org/activity/p/5083/ industrial property developers in singapore] property market, and/or personal property players' acquisitions of industrial properties that had been beforehand owned by JTC.<br><br>Many people, especially the center-class Singaporeans are nonetheless happily buying properties. That stated, my millionaire mentors and I are least focused on shopping for properties, particularly condominiums, because the proposition merely failed our rule that upside must be not less than double the potential draw back. In my books and seminars, I share this thought process that I personally undergo, earlier than making any funding. Since this thought course of is made primarily based on exhausting info, anybody can arrive on the same conclusion by going by way of this process, until he or she already has a biased view of the market. Assess your dedication and work out your price range for the funding ( checking together with your financial individuals make good sense ). 11xxpsf view this project<br><br>One factor now we have in this nation is a large group of "economists," and "market analysts." What's attention-grabbing about this group of real estate market-watchers is that there are two very alternative ways wherein they predict Boomers will influence housing markets over the next decade. Let's take a look at these two opposites and see how every can change the way in which real estate buyers approach their markets. The good news is that real estate traders are ready for either state of affairs, and there's profit in being ready. I'm excited and looking ahead to the opportunities either or both of these conditions will offer; thanks Boomers! Mapletree to further develop beyond Asia Why fortune will favour the brave in Asia's last actual property frontier<br><br>In conclusion, CCS did not find any evidence to this point that there was any single dominant participant, or group of collectively dominant gamers within the industrial property market, and neither did CCS discover that the acquisitions of JTC belongings by private players resulted in a substantial lessening of competitors within the industrial property market in Singapore. One should carefully examine the principles of the Dwelling Proprietor's Association (HOA) that govern the functioning of the apartment improvement. There might be restrictions that won't adhere to your way of life. Pet lovers should examine with the foundations concerning pets within the society. The property tax is calculated by multiplying the Annual Worth (AV) of the property with the prevailing property tax fee Address of property<br><br>The maximum tenure of all new residential property loans will probably be capped at 35 years. As well as, loans exceeding 30 years tenure will face considerably tighter loan-to-worth (LTV) limits. This can apply to both private properties and HDB flats. The brand new rules will take impact from 6 October 2012. Removal of property charge guidelines unlikely to have deep impression Shopper watchdog CASE has welcomed the move, stating that it is not obligatory to have agents facilitate a property transaction. IEA to remove guidelines on property agents' commissions Bayshore, Bedok, Chai Chee Hire Property District 17 Pasir Ris, Simei, Tampines Lease House District 19 Globalisation of commercial real property investment gathers tempo in 2014 as transaction volumes up 23% in Q1 2014<br><br>We eradicated property duties in 2008 as its biggest influence was not on the wealthiest people, who tended to handle their monetary property globally. In doing so, the Authorities defined that property tax could be retained as the only wealth tax as it may very well be structured extra equitably, with the house owners of extra beneficial properties paying more. We additionally do not levy wealth taxes on another types of wealth reminiscent of cash or equity for practical reasons - monies can easily be shifted to comparable belongings in different financial centres, and such taxes will impact Singapore's competitiveness as a monetary centre.<br><br>What's the outlook for traders in these areas, particularly rental property buyers? With few homes for sale and excessive prices, there will likely be an elevated demand for rental properties. Sadly, there will probably be few for sale that will be appropriate for cash stream investing. Nonetheless, the sharp investor who needs to spend money on these markets will look to the sides. Rents might be excessive, one thing we like. The tenants can be forced to maneuver outward from the middle and they'll pay larger rents the nearer they will locate.
 
==Definitions==
A connected dominating set of a graph ''G'' is a set ''D'' of vertices with two properties:
#Any node in ''D'' can reach any other node in ''D'' by a path that stays entirely within ''D''. That is, ''D'' [[induced subgraph|induces]] a connected subgraph of ''G''.
#Every vertex in ''G'' either belongs to ''D'' or is adjacent to a vertex in ''D''. That is, ''D'' is a [[dominating set]] of ''G''.
A '''minimum connected dominating set''' of a graph ''G'' is a connecting dominating set with the smallest possible [[cardinality]] among all connected dominating sets of ''G''. The '''connected domination number''' of ''G'' is the number of vertices in the minimum connected dominating set.<ref>{{citation
| last1 = Sampathkumar | first1 = E.
| last2 = Walikar | first2 = HB
| issue = 6
| journal = J. Math. Phys. Sci
| pages = 607–613
| title = The connected domination number of a graph
| volume = 13
| year = 1979}}.</ref>
 
Any [[spanning tree]] ''T'' of a graph ''G'' has at least two leaves, vertices that have only one edge of ''T'' incident to them. A maximum leaf spanning tree is a spanning tree that has the largest possible number of leaves among all spanning trees of ''G''. The '''max leaf number''' of ''G'' is the number of leaves in the maximum leaf spanning tree.<ref name="ecology">{{citation
| last1 = Fellows | first1 = Michael
| last2 = Lokshtanov | first2 = Daniel
| last3 = Misra | first3 = Neeldhara
| last4 = Mnich | first4 = Matthias
| last5 = Rosamond | first5 = Frances
| last6 = Saurabh | first6 = Saket
| doi = 10.1007/s00224-009-9167-9
| issue = 4
| journal = Theory of Computing Systems
| pages = 822–848
| title = The complexity ecology of parameters: an illustration using bounded max leaf number
| volume = 45
| year = 2009}}.</ref>
 
==Complementarity==
If ''d'' is the connected domination number of an ''n''-vertex graph ''G'', and ''l'' is its max leaf number, then the three quantities ''d'', ''l'', and ''n'' obey the simple equation
:<math>\displaystyle n = d + l.</math><ref name="d92">{{citation
| last = Douglas | first = Robert J.
| doi = 10.1016/0012-365X(92)90130-8
| issue = 1–3
| journal = Discrete Mathematics
| pages = 41–47
| title = NP-completeness and degree restricted spanning trees
| volume = 105
| year = 1992}}.</ref>
 
If ''D'' is a connected dominating set, then there exists a [[spanning tree]] in ''G'' whose leaves include all vertices that are not in ''D'': form a spanning tree of the subgraph induced by ''D'', together with edges connecting each remaining vertex ''v'' that is not in ''D'' to a neighbor of ''v'' in ''D''. This shows that {{nowrap|''l'' ≥ ''n'' &minus; ''d''.}}
 
In the other direction, if ''T'' is any spanning tree in ''G'', then the vertices of ''T'' that are not leaves form a connected dominating set of ''G''. This shows that {{nowrap|''n'' &minus; ''l'' ≥ ''d''.}} Putting these two inequalities together proves the equality {{nowrap|1=''n'' = ''d'' + ''l''.}}
 
Therefore, in any graph, the sum of the connected domination number and the max leaf number equals the total number of vertices.
Computationally, this implies that finding the minimum dominating set is equally difficult to finding a maximum leaf spanning tree.
 
==Algorithms==
It is [[NP-complete]] to test whether there exists a connected dominating set with size less than a given threshold, or equivalently to test whether there exists a spanning tree with at least a given number of leaves. Therefore, it is believed that the minimum connected dominating set problem and the maximum leaf spanning tree problem cannot be solved in polynomial time.
 
When viewed in terms of approximation algorithms, connected domination and maximum leaf spanning trees are not the same: approximating one to within a given [[approximation ratio]] is not the same as approximating the other to the same ratio.
There exists an approximation for the minimum connected dominating set that achieves a factor of {{nowrap|2 ln &Delta; + O(1)}}, where &Delta; is the maximum degree of a vertex in G.<ref>{{citation
| last1 = Guha | first1 = S.
| last2 = Khuller | first2 = S.
| doi = 10.1007/PL00009201
| issue = 4
| journal = Algorithmica
| pages = 374–387
| title = Approximation algorithms for connected dominating sets
| volume = 20
| year = 1998}}.</ref>
The maximum leaf spanning tree problem is [[MAX-SNP]] hard, implying that no [[polynomial time approximation scheme]] is likely.<ref>{{citation
| last1 = Galbiati | first1 = G.
| last2 = Maffioli | first2 = F.
| last3 = Morzenti | first3 = A.
| doi = 10.1016/0020-0190(94)90139-2
| issue = 1
| journal = Information Processing Letters
| pages = 45–49
| title = A short note on the approximability of the maximum leaves spanning tree problem
| volume = 52
| year = 1994}}.</ref> However, it can be approximated to within a factor of 2 in polynomial time.<ref>{{citation
| last = Solis-Oba | first = Roberto
| contribution = 2-approximation algorithm for finding a spanning tree with maximum number of leaves
| doi = 10.1007/3-540-68530-8_37
| pages = 441–452
| publisher = Springer-Verlag
| series = Lecture Notes in Computer Science
| title = [[European Symposium on Algorithms|Proc. 6th European Symposium on Algorithms (ESA'98)]]
| volume = 1461
| year = 1998}}.</ref>
 
==Applications==
Connected dominating set are useful in the computation of [[routing]] for [[mobile ad hoc network]]s. In this application, a small connected dominating set is used as a backbone for communications, and nodes that are not in this set communicate by passing messages through neighbors that are in the set.<ref>{{citation
| last1 = Wu | first1 = J.
| last2 = Li | first2 = H.
| contribution = On calculating connected dominating set for efficient routing in ad hoc wireless networks
| doi = 10.1145/313239.313261
| pages = 7–14
| publisher = ACM
| title = Proceedings of the 3rd International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications
| year = 1999}}.</ref>
 
The max leaf number has been employed in the development of [[fixed-parameter tractability|fixed-parameter tractable]] [[algorithm]]s: several NP-hard optimization problems may be solved in polynomial time for graphs of bounded max leaf number.<ref name="ecology"/>
 
==References==
{{reflist}}
 
[[Category:Computational problems in graph theory]]
[[Category:Graph connectivity]]

Latest revision as of 21:18, 19 December 2014

CCS has obtained feedback that the business community has faced sharp will increase in industrial property costs and rentals in recent years. The concerns were that these increases had been attributable to the growing presence of REITs in the industrial property developers in singapore property market, and/or personal property players' acquisitions of industrial properties that had been beforehand owned by JTC.

Many people, especially the center-class Singaporeans are nonetheless happily buying properties. That stated, my millionaire mentors and I are least focused on shopping for properties, particularly condominiums, because the proposition merely failed our rule that upside must be not less than double the potential draw back. In my books and seminars, I share this thought process that I personally undergo, earlier than making any funding. Since this thought course of is made primarily based on exhausting info, anybody can arrive on the same conclusion by going by way of this process, until he or she already has a biased view of the market. Assess your dedication and work out your price range for the funding ( checking together with your financial individuals make good sense ). 11xxpsf view this project

One factor now we have in this nation is a large group of "economists," and "market analysts." What's attention-grabbing about this group of real estate market-watchers is that there are two very alternative ways wherein they predict Boomers will influence housing markets over the next decade. Let's take a look at these two opposites and see how every can change the way in which real estate buyers approach their markets. The good news is that real estate traders are ready for either state of affairs, and there's profit in being ready. I'm excited and looking ahead to the opportunities either or both of these conditions will offer; thanks Boomers! Mapletree to further develop beyond Asia Why fortune will favour the brave in Asia's last actual property frontier

In conclusion, CCS did not find any evidence to this point that there was any single dominant participant, or group of collectively dominant gamers within the industrial property market, and neither did CCS discover that the acquisitions of JTC belongings by private players resulted in a substantial lessening of competitors within the industrial property market in Singapore. One should carefully examine the principles of the Dwelling Proprietor's Association (HOA) that govern the functioning of the apartment improvement. There might be restrictions that won't adhere to your way of life. Pet lovers should examine with the foundations concerning pets within the society. The property tax is calculated by multiplying the Annual Worth (AV) of the property with the prevailing property tax fee Address of property

The maximum tenure of all new residential property loans will probably be capped at 35 years. As well as, loans exceeding 30 years tenure will face considerably tighter loan-to-worth (LTV) limits. This can apply to both private properties and HDB flats. The brand new rules will take impact from 6 October 2012. Removal of property charge guidelines unlikely to have deep impression Shopper watchdog CASE has welcomed the move, stating that it is not obligatory to have agents facilitate a property transaction. IEA to remove guidelines on property agents' commissions Bayshore, Bedok, Chai Chee Hire Property District 17 Pasir Ris, Simei, Tampines Lease House District 19 Globalisation of commercial real property investment gathers tempo in 2014 as transaction volumes up 23% in Q1 2014

We eradicated property duties in 2008 as its biggest influence was not on the wealthiest people, who tended to handle their monetary property globally. In doing so, the Authorities defined that property tax could be retained as the only wealth tax as it may very well be structured extra equitably, with the house owners of extra beneficial properties paying more. We additionally do not levy wealth taxes on another types of wealth reminiscent of cash or equity for practical reasons - monies can easily be shifted to comparable belongings in different financial centres, and such taxes will impact Singapore's competitiveness as a monetary centre.

What's the outlook for traders in these areas, particularly rental property buyers? With few homes for sale and excessive prices, there will likely be an elevated demand for rental properties. Sadly, there will probably be few for sale that will be appropriate for cash stream investing. Nonetheless, the sharp investor who needs to spend money on these markets will look to the sides. Rents might be excessive, one thing we like. The tenants can be forced to maneuver outward from the middle and they'll pay larger rents the nearer they will locate.

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