The Connected P -Median Problem on Cactus Graphs

Abstract

This study deals with the facility location problem of locating a set $V_p$ of $p$ facilities on a graph such that the subgraph induced by $V_p$ is connected. We consider the connected $p$ -median problem on a cactus graph $G$ whose vertices and edges have nonnegative weights. The aim of a connected $p$ -median problem is to minimize the sum of weighted distances from every vertex of a graph to the nearest vertex in $V_p$ . We provide an $O\left(n^2{p}^2\right)$ time algorithm for the connected $p$ -median problem, where $n$ is the number of vertices.