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

In this paper, we present an algorithm for computing the maximum clique in the visibility graph G of a simple polygon P   in O(n2e)O(n2e) time, where n and e are number of vertices and edges of G   respectively. We also present an O(ne)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.