Degree of reaction: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
No edit summary
en>Raj.iitb
Line 1: Line 1:
A '''kinetic convex hull''' data structure is a [[kinetic data structure]] that maintains the [[convex hull]] of a set of continuously moving points.<ref name="BGH99" />


==The 2D case==
The best known data structure for the 2 dimensional kinetic convex hull problem is by Basch, [[Leonidas J. Guibas|Guibas]], and Hershberger. This data structure is [[Kinetic data structure#Performance|responsive]], [[Kinetic data structure#Performance|efficient]], [[Kinetic data structure#Performance|compact]] and [[Kinetic data structure#Performance|local]].<ref name="BGH99" />


===The data structure===
will help to provide for your family in the event that either of you dies, which can be useful if you need to pay off a mortgage or have dependents who were heavily reliant on the income of your partner. Are you thinking about buying short term health insurance to save some money. The sort of policy is called no health check term insurance and can be instantly processed. For more inforformation about our dental insurance quotes,click and get details. Some people like term insurance because they figure they get the coverage at the lowest rate. Do you have a plan in place to protect your family financially if you should die prematurely. In the event you loved this information and you want to receive more information relating to [http://www.termlifepolicy.com/insurance-companies/general-re-life-corporation.html termlifepolicy.com] please visit our website. There are a lot of people who need the benefits provided by a term life insurance policy that could also benefit from a whole life policy.  <br><br>My Term Life Insurance helps to provide potential life insurance consumers with all of the information that they need in order to make the right choice to purchase a means to safeguard themselves and their family members. Term-life policies are good if you have a specific purpose in mind. The main element is that you can give your family a sufficient sum to collect when you pass away. Most importantly, many policies have clauses that forbid writing the policy in trust. Go to that drawer where you keep all your financial papers, you know the drawer, and dig up your Life Insurance policy. A whole life policy might cost ten times that amount. In simple words if we say, life insurance plays a dual role in your life, saving for life. <br><br>On a term policy, the inexpensive premium that you pay only guarantees you a payout if you die during the period of time the insurance lasts. Most people with life insurance have term life insurance. So consider very strongly sticking with simple term insurance. Keep the retirement and financial savings completely separate from each other. Upon the loss of a loved one, life insurance offers security for those members of the family who were left out. If you meet with an unfortunate death, then your family will not have the burden of the mortgage debt. This is a major financial decision, and it deserves a lot of research time. <br><br>Let's first look at the reasons your life insurance will not pay a claim. However, if something happens most people don't have the funds to cover a car accident, including bodily injury. The city is popular among visitors for its night life. Hence, in order to combat total monetary loss, considering that the i. By that age, you should be free from all liabilities. These term life insurance companies have spent a lot of money advertising their message during prime time. Term life insurance policies have a knack for boasting cheap rates, but this simply will not be beneficial for you if only one person in one hundred is actually eligible for such an outstanding rate. <br><br>Yearly renewable term can be looked at as a one year term which you have the option of renewing each year at a higher premium. 5 - Look at the underwriting on each term life [http://www.tumblr.com/tagged/insurance+quote insurance quote] that you consider. 1 trillion, based on a 2014 survey by the Financial Services Council and Met - Life). Kotak Life Insurance plan technique is a significant reasonable tool for the owner since this technique is designed to provide an sufficient secure to a personal. After paying premiums for a set number of years, permanent policies  will start to pay money back to their policy holder. The 15 year term policy can also be considered a low cost term life insurance policy. But, skillfully managing this type of policy can lead you to a new bucket of money that flows through your world.  <br><br>[http://Www.dict.cc/englisch-deutsch/Insurance.html Insurance] for Life with the Possibility of Withdrawing Funds. Do you know that 1-in-5 Australian families are going to experience unexpected illness, accidents or even death of a parent (based on a 2010 report by Lifewise and National Centre for Social and Economic Modelling (NATSEM)). If you have a husband who works and a wife that takes care of the children, the wife is dependent upon the husband for income and needs life insurance on the husband. "How do I get my foot in the door, so I'm in front of a new prospect. In case of any fatal event, investment in term life insurance will cover your family against financial troubles. Some customers prefer more flexibility and for that reason, some insurance companies will offer them an option called decreasing term life insurance. How can this happen you wonder, let me explain how these policies work. <br> <br> Larger payout amounts are recommended for people with dependents who need their financial support. This is money that the insurance coverage company is investing on your behalf, when you hear individuals speak about borrowing towards the cash value of their insurance coverage this is what they are talking about. Some buyers agonize over the decision as to which is best. You can seek the professional help of your brokers and financial advisers since these industry experts are aware of what you should obtain first. Fortunately, life insurance comes in 2 basic types: whole life and term life. 2) If you purchase a replacement policy or convert your term coverage to a whole life policy, your new rates will be based on your age at the time of conversion or replacement. Term life insurance offers the most cost effective way to gain the perfect insurance coverage, because, dissimilar to permanent life insurance, it demands no cash value.
The [[Duality (projective geometry)|dual]] of a convex hull of a set of points is the upper and lower envelopes of the dual set of lines. Therefore, maintaining the upper and lower envelopes of a set of moving lines is equivalent to maintaining the convex hull of a set of moving points. Computing upper and lower envelopes are equivalent problems, so computing the upper envelope of a set of lines is equivalent to computing the convex hull of a set of moving points.
The upper envelope of a set of static lines can be computed using a [[divide and conquer algorithm]] which partitions the lines into two sets of equal size, calls itself recursively on the two sets to find their upper envelopes, and then merges the two resulting upper envelopes. The merge step is performed using a [[Sweep line algorithm|vertical line sweep]]. Call the first set of points blue and the second set of points red.
 
The standard line sweep algorithm for merging upper envelopes sweeps though all of vertices of the red and blue upper envelopes, from left to right. The most recently encountered red and blue points are maintained as the line sweeps. When a point is encountered, the algorithm checks if the point is above or below the segment following the last encountered point of the opposite color. If it is above, that point is added to the merged upper envelope. If it of a different color than the last added point, the red and blue envelopes have crossed, so the intersection point is also added to the merged upper envelope.<ref>John Hershberger, Finding the upper envelope of n line segments in O(n log n) time,Information Processing Letters Volume 33, Issue 4, 21 December 1989, Pages 169–174</ref>
 
The sequence of edges and vertices resulting from this algorithm is only dependent on the ordering of points, and the results of the line-point comparisons. Thus, the result can be certified with the following certificates:
*x-certificates (<math><_x</math>) are used to certify the order the vertices of the red and blue envelopes. They are the certificates for a [[kinetic sorted list]] on the set of vertices. Since each point involves 2 lines, and the certificate involves 2 points, each certificate involves 4 lines.
*y-certificates (<math><_y</math>) are used certify that a vertex is above or below an edge. The certificates appear for all comparisons that would occur during the algorithm.
As long as all of these certificates are hold, the merge steps will be executed identically, so the resulting upper envelope will be the same. A kinetic data structure for upper envelopes can be created by using these certificates to certify the static upper envelope algorithm. However, this scheme is not local, because one line many be involved in many y-certificates if it remains on top or bottom as many points from the other envelope are encountered.
 
Thus, it is necessary to introduce a s-certificates (<math><_s</math>) which certifies that the slope of a line is greater than or less than the slope of another line.  
Having the following certificates for all points ab is sufficient to certify the sequence of edges and vertices resulting from a merge, with only O(1) certificates per line:<ref name="BGH99" />[[File:Kinetic convex hull, detection of intersections.png|thumb|540px|right|alt=A picture of the certificates in several difference cases|The certificates certify structure of the intersection of the red and blue envelopes by certifying intersections(top left) or the absence of intersections(top right and bottom). The arrows indicate which elements are being compared by the certificate.]]
#<math>x[ab]</math>: <math>ab<_x ab.next</math>. <math>ab.next</math> denotes vertex closest to <math>ab</math> on its right. This certificate is stored for all points <math>ab</math> which have a different color than the point, <math>ab.next</math>, which follows them.
#<math>yli[ab]</math>: <math>ab<_y ce(ab)</math> or <math>ab>_y ce(ab)</math>. This certificate is stored for all points <math>ab</math> such that <math>b</math> intersects <math>ce(ab)</math>. <math>ce(ab)</math> denotes the contender edge of <math>ab</math>, the edge from the other envelope that is above or below <math>ab</math>.
#<math>yri[lb]</math>: <math>ab<_y ce(ab)</math> or <math>ab>_y ce(ab)</math>. This certificate is stored for all points <math>ab</math> such that <math>a</math>  intersects <math>ce(ab)</math>.
#<math>yt[ab]</math>: <math>ce(ab)<_yab</math>. This certificate is stored for all points <math>ab</math> for which <math>a<_sce(ab)<_s b</math> and <math>ce(ab)<_yab</math>.
#<math>srt[ab]</math>: <math>a<_sce(ab)</math>. This certificate is stored for all points <math>ab</math> for which <math>a<_sce(ab)<_s b</math> and <math>ce(ab)<_yab</math>.
#<math>srt[ab]</math>: <math>ce(ab)<_s b</math>. This certificate is stored for all points <math>ab</math> for which <math>a<_sce(ab)<_s b</math> and <math>ce(ab)<_yab</math>.
#<math>sl[ab]</math>: <math>b<_sce(ab)</math>. This certificate is stored for all points <math>ab</math> for which <math>b<_sce(ab)</math> and <math>ab<_yce(ab)</math>.
#<math>sr[ab]</math>: <math>ce(ab)<_sa</math>. This certificate is stored for all points <math>ab</math> for which <math>ce(ab)<_sa</math> and <math>ab<_yce(ab)</math>.
 
The first certificate, <math>x[ab]</math>, certifies the x-ordering of the points in the red and blue envelopes. The second and third certificates, <math>yli[ab]</math> and <math>yri[ab]</math>, certify intersections of the red and blue envelopes. The remaining 5 certificates, <math>yt[ab]</math>, <math>srt[ab]</math>, <math>srt[ab]</math>, <math>sl[ab]</math>, and <math>sr[ab]</math> place edges that are not in the upper envelopes in the sequence of slopes of the edges that are above it. If the slope is at the start or end of the sequence, <math>sl</math> or <math>sr</math> certify this. If it is in the middle of the sequence  <math>slt</math>, and <math>srt</math> certify this, and <math>yt</math> certifies that the intersection point of the two lines that the edge's slope is in between, is above it. These one or three certificates suffice to prove that all of the edges are above this line. Unlike the previous scheme all lines are only involved in a constant number of certificates. Whenever of these certificates fail, the merged envelope and certificates can be updated in O(1) time.
 
The kinetic data structure for convex hull is constructed by using these certificates to certify the recursive merge of the upper envelopes. Whenever certificates fail, their merge is updated, and if the envelope resulting from the merge changes, the changes are propagated up through all merges that depend on the result of the merge.<ref name="BGH99" />
 
=== Performance ===
This data structure is [[Kinetic data structure#Performance|responsive]], [[Kinetic data structure#Performance|local]], [[Kinetic data structure#Performance|compact]], and [[Kinetic data structure#Performance|efficient]]. This is due to the logarithmic depth of the merges used to certify the upper envelope.<ref name="BGH99" />
*'''Responsive:''' When a certificate fails, it takes O(1) to fix the merge it certifies. If the resulting envelope changes, the change must be propagated up to all merges that depend on the result of the changed merge. There are O(log n) such mergers, so the update can can be performed in O(log n) time total.
*'''Local:''' Each line is involved in a most O(log n) certificates. This is because each line is involved in a constant number of certificates in each merge, and each line is in O(log n) merges total.
*'''Compactness:''' The maximum number of certificates used in this data structure is O(n log n). This is because each merge involves a number of certificates linear to the number of lines merged. Certifying an upper envelope of n lines requires certificates for the merge upper envelope of the two subsets of n/2 lines, and certificates for the merge of the envelopes. Thus the number of certificates, C(n), required to certify the  upper envelope of n lines satisfies the recurrence C(n)=2C(n/2)+O(n), with C(1)=O(1). By the [[master theorem]] the C(n)=O(n log n).
*'''Efficiency:''' The maximum number of events processed by this algorithm on [[Kinetic data structure#Types of Trajectories|algebraic]] or [[Kinetic data structure#Types of Trajectories|pseudo-algebraic]] trajectories is near quadratic, <math>O(n^{2+\epsilon})</math> for all <math>\epsilon>0</math>.<ref name="ASS96">
P. K. Agarwal, O. Schwarzkopf, and Micha Sharir. The overlay of lower envelopes and its applications. Discrete Comput. Geom., 15:1–13, 1996.
</ref><ref name="Sha94">
Micha Sharir. Almost tight upper bounds for lower envelopes in higher dimensions. Discrete Comput. Geom., 12:327–345, 1994.
</ref> Convex hulls of linearly moving points can change <math>\Omega(n^2)</math> times.<ref name="AGHV01">
Pankaj K. Agarwal, Leonidas J. Guibas, John Hershberger, and Eric Veach. Maintaining the extent of a moving point set. Discrete and Computational Geometry, 26(3):353–374, 2001.
</ref> Thus this data structure is efficient.
 
==Higher dimensions==
Finding an [[Kinetic data structure#Performance|efficient]] kinetic data structure for maintaining the convex hull of moving points in dimensions higher than 2 is an open problem.<ref name="BGH99">
Julien Basch, Leonidas J. Guibas, and John Hershberger. Data structures for mobile data. J. Algorithms, 31(1):1{28, 1999. [http://graphics.stanford.edu/courses/cs268-11-spring/notes/kinetic.pdf]
</ref>
 
== Related Problems ==
Kinetic convex hull can be used to solve the following related problems:<ref>P. K. Agarwal, L. J. Guibas, J. Hershberger, and E. Verach. Maintaining the extent of a moving set of points.</ref>
*[[Kinetic diameter]]
*[[Kinetic width]]
*[[Kinetic minimum box]]
*[[Kinetic smallest enclosing disk]]
 
== References ==
{{Reflist}}
 
[[Category:Articles created via the Article Wizard]]
[[Category:Kinetic data structures]]
[[Category:Convex hull algorithms]]

Revision as of 13:43, 7 February 2014


will help to provide for your family in the event that either of you dies, which can be useful if you need to pay off a mortgage or have dependents who were heavily reliant on the income of your partner. Are you thinking about buying short term health insurance to save some money. The sort of policy is called no health check term insurance and can be instantly processed. For more inforformation about our dental insurance quotes,click and get details. Some people like term insurance because they figure they get the coverage at the lowest rate. Do you have a plan in place to protect your family financially if you should die prematurely. In the event you loved this information and you want to receive more information relating to termlifepolicy.com please visit our website. There are a lot of people who need the benefits provided by a term life insurance policy that could also benefit from a whole life policy.

My Term Life Insurance helps to provide potential life insurance consumers with all of the information that they need in order to make the right choice to purchase a means to safeguard themselves and their family members. Term-life policies are good if you have a specific purpose in mind. The main element is that you can give your family a sufficient sum to collect when you pass away. Most importantly, many policies have clauses that forbid writing the policy in trust. Go to that drawer where you keep all your financial papers, you know the drawer, and dig up your Life Insurance policy. A whole life policy might cost ten times that amount. In simple words if we say, life insurance plays a dual role in your life, saving for life.

On a term policy, the inexpensive premium that you pay only guarantees you a payout if you die during the period of time the insurance lasts. Most people with life insurance have term life insurance. So consider very strongly sticking with simple term insurance. Keep the retirement and financial savings completely separate from each other. Upon the loss of a loved one, life insurance offers security for those members of the family who were left out. If you meet with an unfortunate death, then your family will not have the burden of the mortgage debt. This is a major financial decision, and it deserves a lot of research time.

Let's first look at the reasons your life insurance will not pay a claim. However, if something happens most people don't have the funds to cover a car accident, including bodily injury. The city is popular among visitors for its night life. Hence, in order to combat total monetary loss, considering that the i. By that age, you should be free from all liabilities. These term life insurance companies have spent a lot of money advertising their message during prime time. Term life insurance policies have a knack for boasting cheap rates, but this simply will not be beneficial for you if only one person in one hundred is actually eligible for such an outstanding rate.

Yearly renewable term can be looked at as a one year term which you have the option of renewing each year at a higher premium. 5 - Look at the underwriting on each term life insurance quote that you consider. 1 trillion, based on a 2014 survey by the Financial Services Council and Met - Life). Kotak Life Insurance plan technique is a significant reasonable tool for the owner since this technique is designed to provide an sufficient secure to a personal. After paying premiums for a set number of years, permanent policies will start to pay money back to their policy holder. The 15 year term policy can also be considered a low cost term life insurance policy. But, skillfully managing this type of policy can lead you to a new bucket of money that flows through your world.

Insurance for Life with the Possibility of Withdrawing Funds. Do you know that 1-in-5 Australian families are going to experience unexpected illness, accidents or even death of a parent (based on a 2010 report by Lifewise and National Centre for Social and Economic Modelling (NATSEM)). If you have a husband who works and a wife that takes care of the children, the wife is dependent upon the husband for income and needs life insurance on the husband. "How do I get my foot in the door, so I'm in front of a new prospect. In case of any fatal event, investment in term life insurance will cover your family against financial troubles. Some customers prefer more flexibility and for that reason, some insurance companies will offer them an option called decreasing term life insurance. How can this happen you wonder, let me explain how these policies work.

Larger payout amounts are recommended for people with dependents who need their financial support. This is money that the insurance coverage company is investing on your behalf, when you hear individuals speak about borrowing towards the cash value of their insurance coverage this is what they are talking about. Some buyers agonize over the decision as to which is best. You can seek the professional help of your brokers and financial advisers since these industry experts are aware of what you should obtain first. Fortunately, life insurance comes in 2 basic types: whole life and term life. 2) If you purchase a replacement policy or convert your term coverage to a whole life policy, your new rates will be based on your age at the time of conversion or replacement. Term life insurance offers the most cost effective way to gain the perfect insurance coverage, because, dissimilar to permanent life insurance, it demands no cash value.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Degree_of_reaction&oldid=270256"