Visibility testing and counting

•Given a set of n disjoint line segments and a segment s, we consider 2 problems.•Visibility testing problem is to check whether a given point p is visible to s.•Visibility counting problem is to count the number of segments visible from p.•We give a new randomized algorithm for VTP and an approxima...

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Published in:	Information processing letters Vol. 115; no. 9; pp. 649 - 654
Main Authors:	Alipour, Sharareh, Ghodsi, Mohammad, Zarei, Alireza, Pourreza, Maryam
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.09.2015 Elsevier Sequoia S.A
Subjects:	Algorithms Approximation algorithm Computational geometry Computer science Information processing Mathematical problems Quadratic programming Randomized algorithm Studies Test methods Visibility Computational geometry Visibility Randomized algorithm Approximation algorithm
ISSN:	0020-0190, 1872-6119
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Abstract	•Given a set of n disjoint line segments and a segment s, we consider 2 problems.•Visibility testing problem is to check whether a given point p is visible to s.•Visibility counting problem is to count the number of segments visible from p.•We give a new randomized algorithm for VTP and an approximation algorithm for VCP.•We present our experimental results. For a set of n disjoint line segments S in R2, the visibility testing problem (VTP) is to test whether the query point p sees a query segment s∈S. For this configuration, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from any query point p can be computed quickly. In this paper, we solve VTP in expected logarithmic query time using quadratic preprocessing time and space. Moreover, we propose a (1+δ)-approximation algorithm for VCP using at most quadratic preprocessing time and space. The query time of this method is Oϵ(1δ2n) where Oϵ(f(n))=O(f(n)nϵ) and ϵ>0 is an arbitrary constant number.
AbstractList	•Given a set of n disjoint line segments and a segment s, we consider 2 problems.•Visibility testing problem is to check whether a given point p is visible to s.•Visibility counting problem is to count the number of segments visible from p.•We give a new randomized algorithm for VTP and an approximation algorithm for VCP.•We present our experimental results. For a set of n disjoint line segments S in R2, the visibility testing problem (VTP) is to test whether the query point p sees a query segment s∈S. For this configuration, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from any query point p can be computed quickly. In this paper, we solve VTP in expected logarithmic query time using quadratic preprocessing time and space. Moreover, we propose a (1+δ)-approximation algorithm for VCP using at most quadratic preprocessing time and space. The query time of this method is Oϵ(1δ2n) where Oϵ(f(n))=O(f(n)nϵ) and ϵ>0 is an arbitrary constant number. For a set of n disjoint line segments S in R..., the visibility testing problem (VTP) is to test whether the query point p sees a query segment s...S. For this configuration, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from any query point p can be computed quickly. This paper solves VTP in expected logarithmic query time using quadratic preprocessing time and space. Moreover, we propose a (1+d)-approximation algorithm for VCP using at most quadratic preprocessing time and space. The query time of this method is ... where ...(f(n))=O(f(n)n...) and ...>0 is an arbitrary constant number. (ProQuest: ... denotes formulae/symbols omitted.)
Author	Alipour, Sharareh Ghodsi, Mohammad Pourreza, Maryam Zarei, Alireza
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SubjectTerms	Algorithms Approximation algorithm Computational geometry Computer science Information processing Mathematical problems Quadratic programming Randomized algorithm Studies Test methods Visibility
Title	Visibility testing and counting
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