Computing the maximum clique in the visibility graph of a simple polygon

Authors:
Subir Kumar Ghosh;Thomas Caton Shermer;Binay Kumar Bhattacharya;Partha Pratim Goswami
Affiliations:
School of Computer Science, Tata Institute of Fundamental Research, Mumbai 400005, India;School of Computing Science, Simon Fraser University, Burnaby, B.C. Canada V5A 1S6;School of Computing Science, Simon Fraser University, Burnaby, B.C. Canada V5A 1S6;Department of Computer Science and Engineering, University of Kalyani, Nadia, West Bengal 742135, India
Venue:
Journal of Discrete Algorithms
Year:
2007

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Abstract

In this paper, we present an algorithm for computing the maximum clique in the visibility graph G of a simple polygon P in O(n^2e) time, where n and e are number of vertices and edges of G respectively. We also present an O(ne) time algorithm for computing the maximum hidden vertex set in the visibility graph G of a convex fan P. We assume in both algorithms that the Hamiltonian cycle in G that corresponds to the boundary of P is given as an input along with G.