Approximating Soft-Capacitated Facility Location Problem With Uncertainty

TL;DR

This paper improves approximation algorithms for soft-capacitated facility location problems under uncertainty, introducing new models and leveraging advanced techniques to achieve constant-factor solutions.

Contribution

It presents novel models for soft-capacitated facility location with uncertainty and develops the first constant-factor approximation algorithms for these models.

Findings

Improved approximation ratios of 2.206 and α+4 for related stochastic and robust problems.

Introduction of two new models: 2-Stage and Robust Soft-Capacitated Facility Location.

Development of constant-factor approximation algorithms using reductions, randomized thresholding, and clustering techniques.

Abstract

We first show that a better analysis of the algorithm for The Two-Sage Stochastic Facility Location Problem from Srinivasan \cite{sri07} and the algorithm for The Robust Fault Tolerant Facility Location Problem from Byrka et al \cite{bgs10} can render improved approximation factors of 2.206 and \alpha+4 where \alpha is the maximum number an adversary can close, respectively, and which are the best ratios so far. We then present new models for the soft-capacitated facility location problem with uncertainty and design constant factor approximation algorithms to solve them. We devise the stochastic and robust approaches to handle the uncertainty incorporated into the original model. Explicitly, in this paper we propose two new problem, named The 2-Stage Soft-Capacitated Facility Location Problem and The Robust Soft-Capacitated Facility Location Problem respectively, and present constant factor approximation algorithms for them both. Our method uses reductions between facility location problems and linear-cost models, the randomized thresholding technique of Srinivasan \cite{sri07} and the filtering and clustering technique of Byrka et al \cite{bgs10}.