Loading...

Visibility testing and counting

Alipour, S ; Sharif University of Technology | 2011

412 Viewed
  1. Type of Document: Article
  2. DOI: 10.1007/978-3-642-21204-8_36
  3. Publisher: 2011
  4. Abstract:
  5. For a set of n disjoint line segments S in R2, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from a query point p can be computed quickly. For this configuration, the visibility testing problem (VTP) is to test whether p sees a fixed segment s. These problems can be solved in logarithmic query time by using O(n4) preprocessing time and space. In this paper, we approximately solve this problem using quadratic preprocessing time and space. Our methods are superior to current approximation algorithms in terms of both approximation factor and preprocessing cost. In this paper, we propose a 2-approximation algorithm for the VCP using at most quadratic preprocessing time and space. The query time of this method is Oε(n2/√k) where k is the preprocessing time and Oε(f(n)) = O(f(n)n ε). We also solve the VTP in expected logarithmic query time using quadratic time and space
  6. Keywords:
  7. Approximation factor ; Counting problems ; Line segment ; Preprocess ; Preprocessing time ; Quadratic time ; Query points ; Query time ; Computational geometry ; Problem solving ; Visibility ; Approximation algorithms
  8. Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 28 May 2011 through 31 May 2011, Jinhua ; Volume 6681 LNCS , 2011 , Pages 343-351 ; 03029743 (ISSN) ; 9783642212031 (ISBN)
  9. URL: http://link.springer.com/chapter/10.1007%2F978-3-642-21204-8_36