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

Content Provider	ACM Digital Library
Author	Aronov, Boris Abam, Mohammad Ali De Berg, Mark Khosravi, Amirali
Abstract	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 (non-rectilinear) 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.
Starting Page	407
Ending Page	416
Page Count	10
File Format	PDF
ISBN	9781450306829
DOI	10.1145/1998196.1998263
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-13
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Computational geometry Stabbing number Approximation algorithms Steiner triangulations Rectangular decompositions Polygons
Content Type	Text
Resource Type	Article

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