Can visibility graphs be represented compactly?

Pankaj K. Agarwal, Noga Alon, Boris Aronov, Subhash Suri

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 well-known 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).

Original languageEnglish
Title of host publicationProceedings of the 9th Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery (ACM)
Pages338-347
Number of pages10
ISBN (Print)0897915828, 9780897915823
DOIs
StatePublished - 1993
Externally publishedYes
EventProceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA
Duration: 19 May 199321 May 1993

Publication series

NameProceedings of the 9th Annual Symposium on Computational Geometry

Conference

ConferenceProceedings of the 9th Annual Symposium on Computational Geometry
CitySan Diego, CA, USA
Period19/05/9321/05/93

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