p-median location interdiction on trees

TL;DR

This paper studies the complexity of p-median interdiction on trees, proving NP-hardness in general but providing polynomial-time algorithms for specific cases like unit-length trees and path graphs with multiple interdictions.

Contribution

It establishes NP-hardness of p-median interdiction on acyclic graphs and offers new polynomial-time algorithms for interdiction on trees and path graphs under certain conditions.

Findings

NP-hardness of the problem on acyclic graphs

Polynomial-time algorithm for interdiction on trees with unit lengths

Algorithms for interdiction on path graphs with multiple edges

Abstract

In p-median location interdiction the aim is to find a subset of edges in a graph, such that the objective value of the p-median problem in the same graph without the selected edges is as large as possible. We prove that this problem is NP-hard even on acyclic graphs. Restricting the problem to trees with unit lengths on the edges, unit interdiction costs, and a single edge interdiction, we provide an algorithm which solves the problem in polynomial time. Furthermore, we investigate path graphs with unit and arbitrary lengths. For the former case, we present an algorithm, where multiple edges can get interdicted. Furthermore, for the latter case, we present a method to compute an optimal solution for one interdiction step which can also be extended to multiple interdicted edges.