Abstract
Given a simple polygon P with n vertices and a set Q of m points in P, we consider the geodesic k-center problem where we want to find k points, called centers, in P to minimize the maximum geodesic distance of any point of Q to its closest center. In this paper, we focus on the case of k=2 and present an O(m(n+m)log3(n+m))-time algorithm for computing an optimal 2-center of Q with respect to the geodesic distance in P.
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