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Visibility testing and counting

Alipour, S ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ipl.2015.03.009
  3. Publisher: Elsevier , 2015
  4. Abstract:
  5. 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 (1/δ 2√n) where Oε (f(n))=O(f(n)nε) and ε>0 is an arbitrary constant number
  6. Keywords:
  7. Computational geometry ; Visibility ; Arbitrary constants ; Counting problems ; Line segment ; Preprocess ; Preprocessing time ; Query points ; Query segments ; Randomized Algorithms ; Approximation algorithms
  8. Source: Information Processing Letters ; Volume 115, Issue 9 , September , 2015 , Pages 649-654 ; 00200190 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0020019015000484