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Abstract: We consider the problem of representing the visibility graph of line segments as a union of cliques and bipartite cliques. Given a graph G, a family G = fG 1 ; G 2 ; : : : ; G k g is called a clique cover of G if (i) each G i is a clique or a bipartite clique, and (ii) the union of G i is G. The size of the clique cover G is defined as P k i=1 n i , where n i is the number of vertices in G i . Our main result is that there exist visibility graphs of n nonintersecting line segments in the ... (Update)
Context of citations to this paper: More
...graphs have been subject of extensive research. The number of edges [16] the computational complexity [18, 13, 7, 9] storage space [1, 8], and on line updates [6] have been studied for this class of graphs over the past decade. We are interested in the following problem...
.... However, existing geometric range searching results allow us to compress the intersection graph, using biclique covers [1, 14]. Although the technique is familiar, it has not been observed in the current context, and in our opinion, leads to a conceptually cleaner...
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BibTeX entry: (Update)
Pankaj K. Agarwal, N. Alon, B. Aronov, and S. Suri. Can visibility graphs be represented compactly? In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 338--347, 1993. http://citeseer.ist.psu.edu/agarwal93can.html More
@inproceedings{ agarwal93can,
author = "Pankaj K. Agarwal and Noga Alon and Boris Aronov and Subhash Suri",
title = "Can Visibility Graphs be Represented Compactly?",
booktitle = "Symposium on Computational Geometry",
pages = "338-347",
year = "1993",
url = "citeseer.ist.psu.edu/agarwal93can.html" }
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439 An Introduction to the Theory of Numbers (context) - Hardy, Wright - 1959
87 Applications of parametric searching in geometric optimizati.. - Agarwal, Sharir et al. - 1993
60 Algorithms for bichromatic line segment problems and polyhed.. (context) - Chazelle, Edelsbrunner et al.
55 Visibility and intersection problems in plane geometry (context) - Chazelle, Guibas - 1989
42 An output-sensitive algorithm for computing visibility graph.. (context) - Ghosh, Mount - 1991
34 Constructing the visibility graph for n line segments in O (context) - Welzl - 1985
33 Lower bounds on the complexity of polytope range searching (context) - Chazelle - 1989
17 A theorem in finite projective geometry and some application.. (context) - Singer - 1938
17 Lower bounds for the orthogonal range searching: II (context) - Chazelle - 1990
17 A lower bound on the complexity of orthogonal range queries (context) - Fredman - 1981
9 Covering of graphs by complete bipartite subgraphs: complexi.. (context) - Tuza - 1984
6 The biggest diagonal in a simple polygon (context) - Aggarwal, Suri - 1990
6 a problem of Sidon in additive number theory (context) - Erdos, Tur'an - 1941
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