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Approximation algorithms for computing partitions with minimum stabbing number of rectilinear and simple polygons

Abam, M. A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1145/1998196.1998263
  3. Publisher: 2011
  4. Abstract:
  5. Let P be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition for histograms. We also study Steiner triangulations of a simple (nonrectilinear) polygon P. Here the stabbing number is defined as the maximum number of triangles that can be stabbed by any line segment inside P. We give an O(1)-approximation algorithm for the problem of computing a Steiner triangulation with minimum stabbing number
  6. Keywords:
  7. Steiner triangulations ; Line segment ; Number of triangles ; Optimal partitions ; Polygons ; Rectangular decompositions ; Simple polygon ; Stabbing numbers ; Computational geometry ; Triangulation ; Approximation algorithms
  8. Source: Proceedings of the Annual Symposium on Computational Geometry, 13 June 2011 through 15 June 2011 ; June , 2011 , Pages 407-416 ; 9781450306829 (ISBN)
  9. URL: http://dl.acm.org/citation.cfm?doid=1998196.1998263