New Results on the Fault-Tolerant Facility Placement Problem

TL;DR

This paper introduces a 1.7245-approximation algorithm for the Fault-Tolerant Facility Placement problem, extending solutions from related fault-tolerant location problems with a novel reduction technique.

Contribution

It presents a new approximation algorithm for FTFP using a reduction to Fault-Tolerant Facility Location, improving solution quality for this generalized problem.

Findings

Achieved a 1.7245-approximation ratio for FTFP

Developed a reduction technique from FTFP to Fault-Tolerant Facility Location

Enhanced understanding of fault-tolerant facility placement algorithms

Abstract

We studied the Fault-Tolerant Facility Placement problem (FTFP) which generalizes the uncapacitated facility location problem (UFL). In FTFP, we are given a set F of sites at which facilities can be built, and a set C of clients with some demands that need to be satisfied by different facilities. A client $j$ has demand $r_j$. Building one facility at a site $i$ incurs a cost $f_i$, and connecting one unit of demand from client $j$ to a facility at site $i\in\fac$ costs $d_{ij}$. $d_{ij}$'s are assumed to form a metric. A feasible solution specifies the number of facilities to be built at each site and the way to connect demands from clients to facilities, with the restriction that demands from the same client must go to different facilities. Facilities at the same site are considered different. The goal is to find a solution with minimum total cost. We gave a 1.7245-approximation algorithm to the FTFP problem. Our technique is via a reduction to the Fault-Tolerant Facility Location problem, in which each client has demand $r_j$ but each site can have at most one facility built.