Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
Computing the longest diagonal of a simple polygon
Information Processing Letters
An output-sensitive algorithm for computing visibility
SIAM Journal on Computing
Applications of parametric searching in geometric optimization
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A Lower Bound on the Complexity of Orthogonal Range Queries
Journal of the ACM (JACM)
New lower bounds for Hopcroft's problem
Proceedings of the eleventh annual symposium on Computational geometry
Approximating monotone polygonal curves using the uniform metric
Proceedings of the twelfth annual symposium on Computational geometry
Consensus algorithms for the generation of all maximal bicliques
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
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We consider the problem of representing the visibility graph ofline segments as a union of cliques and bipartite cliques. Given a graphG, a family G=G1,G2,&ldots;,Gk is called a cliquecover of G if (i)each Gi is aclique or a bipartite clique, and (ii) the union ofGi isG. The size of the clique coverG is defined as i=1kni, whereni is the numberof vertices inGi. Our mainresult is that there exist visibility graphs ofn nonintersecting line segments inthe plane whose smallest clique cover has size Wn2/log2n. An upper bound of On2/logn on the clique cover follows from a well-known resultin extremal graph theory. On the other hand, we show that the visibilitygraph of a simple polygon always admits a clique cover of sizeOnlog3n, and that there are simple polygons whose visibilitygraphs require a clique cover of size Wnlogn.