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Space-query-time tradeoff for computing the visibility polygon

Nouri, M ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-642-02270-8_14
  3. Publisher: 2009
  4. Abstract:
  5. Computing the visibility polygon, VP, of a point in a polygonal scene, is a classical problem that has been studied extensively. In this paper, we consider the problem of computing VP for any query point efficiently, with some additional preprocessing phase. The scene consists of a set of obstacles, of total complexity O(n). We show for a query point q, VP(q) can be computed in logarithmic time using O(n 4) space and O(n 4 logn) preprocessing time. Furthermore to decrease space usage and preprocessing time, we make a tradeoff between space usage and query time; so by spending O(m) space, we can achieve O(n 2 log √ m/n)/√ m)query time, where n 2≤m≤n 4. These results are also applied to angular sorting of a set of points around a query point. © 2009 Springer Berlin Heidelberg
  6. Keywords:
  7. Visibility polygon ; (1/r)-cutting ; Classical problems ; Logarithmic query time ; Logarithmic time ; Preprocessing phase ; Preprocessing time ; Query points ; Query time ; Space usage ; Space-query-time tradeoff ; Computer science ; Visibility ; Communication channels (information theory)
  8. Source: 3rd International Frontiers of Algorithmics Workshop, FAW 2009, Hefei, 20 June 2009 through 23 June 2009 ; Volume 5598 LNCS , 2009 , Pages 120-131 ; 03029743 (ISSN); 3642022693 (ISBN); 9783642022692 (ISBN)
  9. URL: https://link.springer.com/chapter/10.1007/978-3-642-02270-8_14