On the complexity of the upgrading version of the maximal covering location problem

TL;DR

This paper analyzes the computational complexity of an upgraded maximal covering location problem on networks, identifying cases where it is polynomially solvable and establishing NP-hardness in more general scenarios.

Contribution

It provides complexity results for the upgraded maximal covering location problem on various network structures, including polynomial algorithms for specific cases and NP-hardness proofs.

Findings

Polynomial-time solution for star networks with uniform weights

NP-hardness for non-uniform weights on star networks

Pseudo-polynomial algorithm for single facility problem on trees

Abstract

In this article, we study the complexity of the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem is NP-hard on general networks. However, in some particular cases, we prove that this problem is solvable in polynomial time. The cases of star and path networks combined with different assumptions for the model parameters are analysed. In particular, we obtain that the problem on star networks is solvable in O(nlogn) time for uniform weights and NP-hard for non-uniform weights. On paths, the single facility problem is solvable in O(n^3) time, while the p-facility problem is NP-hard even with uniform costs and upper bounds (maximal upgrading per edge), as well as, integer parameter values. Furthermore, a pseudo-polynomial algorithm is developed for the single facility problem on trees with integer parameters.