The Mixed Center Location Problem

This paper studies a new version of the location problem called the mixed center location problem. Let P be a set of n points in the plane. We first consider the mixed 2-center problem where one of the centers must be in P and solve it in \(O(n^2\log n)\) time. Next we consider the mixed k-center problem where m of the centers are in P. Motivated by two practical constraints, we propose two variations of the problem. We present an exact algorithm, a 2-approximation algorithm and a heuristic algorithm solving the mixed k-center problem. The time complexity of the exact algorithm is \(O(n^{m+O(\sqrt{k-m})})\).