Improved minmax regret 1-center algorithms for cactus networks with c cycles

Abstract

In a facility location problem, if the vertex weights are uncertain one may look for a "robust" solution that minimizes "regret." We present an O(nlogn) (resp. O(cnlogn)) time algorithm for a tree (resp. c-cycle cactus), where n is the number of vertices and c is a constant. Our tree algorithm presents an improvement over the previously known algorithms that run in O(nlog2 n) time. There is no previously published result tailored specifically for a cactus network. The best algorithm for a general network takes O(mn logn) time, where m is the number of edges. © 2014 Springer-Verlag Berlin Heidelberg.