Application of computational geometry to network p-center location problems

In this note we showed that a p(≥ 2)-center location problem in general networks can be transformed to the well known Klee’s measure problem [3]. This resulted in an improved algorithm for the continuous case with running time O(mn2 ∗ n log n). The previous best result for the problem is O(mnα(n) log n) where α(n) is the inverse Ackermann function [9]. When the underlying network is a partial k-tree (k fixed), by exploiting the geometry inherent in the problem we showed that the discrete p-center problem can be solved in O(pn log n) time.