A note on the P - Center problem

Abstract

The p - center problem is to locate p facilities in a network so as to minimize the longest distance between a demand point and its nearest facility. In this paper, we give a construction on a graph G which produces an infinite ascending chain G = G0 ≤ G1 ≤ G2 ≤ ... of graphs containing G such that given any optimal solution X for the p - center problem on G , X is an optimal solution for the p - center problem on i G for any i ≥ 1.