Robust Fault Tolerant uncapacitated facility location

TL;DR

This paper introduces a polynomial-time approximation algorithm for the robust fault-tolerant uncapacitated facility location problem, addressing failures in facilities to optimize costs, and proves the problem's NP-hardness even on trees.

Contribution

It provides the first approximation algorithms for RFTFL with multiple failures and establishes NP-hardness of the problem on trees.

Findings

6.5-approximation for single failure case

1.5 + 7.5α-approximation for multiple failures

NP-hardness on trees even with one failure

Abstract

In the uncapacitated facility location problem, given a graph, a set of demands and opening costs, it is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities. This paper concerns the robust fault-tolerant version of the uncapacitated facility location problem (RFTFL). In this problem, one or more facilities might fail, and each demand should be supplied by the closest open facility that did not fail. It is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities that did not fail, after the failure of up to \alpha facilities. We present a polynomial time algorithm that yields a 6.5-approximation for this problem with at most one failure and a 1.5 + 7.5\alpha-approximation for the problem with at most \alpha > 1 failures. We also show that the RFTFL problem is NP-hard even on trees, and even in the case of a single failure.