A heuristic for the p-center problems in graphs

Given a connected graph G, the vertex and edge sets and their cardinalities are denoted by V(G), E(G), n and m, respectively. It is assumed that every vertex o is assigned a non-negative real number w(o), called the weight of o, and every edge uv is assigned a positive real number a(uo), the length of uo. The lengths determine the distance d(u, o) between any two vertices u and o as the minimal sum of the edge lengths of a u o path. The distance between a vertex o e V(G) and a set X C V(G) is d(o, X) := min{d(o, x ) [ x e X } . A p-set is a set of cardinality p. Given G and p, the p-center problem is to find a p-set X C V(G) such that the objective function, weighted eccentricity,