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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Bibliographic Details
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
Online Access:Get full text
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Summary:•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.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2015.03.009