Constrained Fault-Tolerant Resource Allocation

TL;DR

This paper introduces approximation algorithms for the Constrained Fault-Tolerant Resource Allocation problem, improving solution quality and extending to related problems with constraints on total resources and facility openings.

Contribution

It presents LP-rounding and primal-dual algorithms with new approximation ratios for FTRA and its variants, including the first constant-factor approximation for k-FTRA.

Findings

LP-rounding algorithm achieves a 4-approximation for general metric FTRA.

Uniform FTRA admits a 1.52-approximation primal-dual algorithm.

Constant-factor approximation of 4 for uniform k-FTRA.

Abstract

In the Constrained Fault-Tolerant Resource Allocation (FTRA) problem, we are given a set of sites containing facilities as resources, and a set of clients accessing these resources. Specifically, each site i is allowed to open at most R_i facilities with cost f_i for each opened facility. Each client j requires an allocation of r_j open facilities and connecting j to any facility at site i incurs a connection cost c_ij. The goal is to minimize the total cost of this resource allocation scenario. FTRA generalizes the Unconstrained Fault-Tolerant Resource Allocation (FTRA_{\infty}) [18] and the classical Fault-Tolerant Facility Location (FTFL) [13] problems: for every site i, FTRA_{\infty} does not have the constraint R_i, whereas FTFL sets R_i=1. These problems are said to be uniform if all r_j's are the same, and general otherwise. For the general metric FTRA, we first give an LP-rounding algorithm achieving the approximation ratio of 4. Then we show the problem reduces to FTFL, implying the ratio of 1.7245 from [3]. For the uniform FTRA, we provide a 1.52-approximation primal-dual algorithm in O(n^4) time, where n is the total number of sites and clients. We also consider the Constrained Fault-Tolerant k-Resource Allocation (k-FTRA) problem where additionally the total number of facilities can be opened across all sites is bounded by k. For the uniform k-FTRA, we give the first constant-factor approximation algorithm with a factor of 4. Note that the above results carry over to FTRA_{\infty} and k-FTRA_{\infty}.