The Complete Vertex p-Center Problem
Abstract
The vertex p-center problem consists of locating p facilities among a set of M potential sites such that the maximum distance from any demand to its closest located facility is minimized. The complete vertex p-center problem solves the p-center problem for all p from 1 to the total number of sites, resulting in a multi-objective trade-off curve between the number of facilities and the service distance required to achieve full coverage. This trade-off provides a reference to planners and decision-makers, enabling them to easily visualize the consequences of choosing different coverage design criteria for the given spatial configuration of the problem. We present two fast algorithms for solving the complete p-center problem, one using the classical formulation but trimming variables while still maintaining optimality, the other converting the problem to a location set covering problem and solving for all distances in the distance matrix. We also discuss scenarios where it makes sense to solve the problem via brute-force enumeration. All methods result in significant speed-ups, with the set covering method reducing computation times by many orders of magnitude.
Cite
@article{arxiv.2109.12723,
title = {The Complete Vertex p-Center Problem},
author = {F. Antonio Medrano},
journal= {arXiv preprint arXiv:2109.12723},
year = {2021}
}