Math @ Duke

Publications [#235573] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Alon, N; Aronov, B; Suri, S, Can visibility graphs be represented compactly?,
in Ninth Annual Symposium on Computational Geometry,
Proceedings of the 9th Annual Symposium on Computational Geometry
(1993),
pp. 338347
(last updated on 2018/10/16)
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 = {G1, G2,..., Gk} is called a clique cover of G if (i) each Gi is a clique or a bipartite clique, and (ii) the union of Gi is G. The size of the clique cover G is defined as Σik=1 ni, where ni is the number of vertices in Gi. Our main result is that there exist visibility graphs of n nonintersecting line segments in the plane whose smallest clique cover has size Ω(n2/log2 n). An upper bound of O(n2/log n) on the clique cover follows from a wellknown result in extremal graph theory. On the other hand, we show that the visibility graph of a simple polygon always admits a clique cover a size O(n log3 n), and that there are simple polygons whose visibility graphs require a clique cover of size Ω(n log n).


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