The Constrained 2-Maxian Problem on Cycles

Abstract

This paper deals with p-maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p=2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles.