The Connected p-Centdian Problem on Block Graphs

Abstract

In this paper, we consider the problems of locating p-vertex $$X_p$$Xp on block graphs such that the induced subgraph of the selected p vertices is connected. Two problems are proposed: one problem is to minimizes the sum of its weighted distances from all vertices to $$X_p$$Xp, another problem is to minimize the maximum distance from each vertex in $$V-X_p$$V-Xp to $$X_p$$Xp and at the same time to minimize the sum of its distances from all vertices. We prove that the first problem is linearly solvable on block graphs with unit edge length. For the second problem, it is shown that the set of Pareto-optimal solutions of the two criteria has cardinality not greater than n, and can be obtained in $$On^2$$On2 time, where n is the number of vertices of the block graph.