Improved Approximation Algorithm for Fault-Tolerant Facility Placement

Abstract

We consider the Fault-Tolerant Facility Placement problem (F T F P ), which is a generalization of the classical Uncapacitated Facility Location problem (U F L). In the F T F P problem we have a set of clients C and a set of facilities F . Each facility i ∈ F can be opened many times. For each opening of facility i we pay fi ≥ 0. Our goal is to connect each client j ∈ C with rj ≥ 1 open facilities in a way that minimizes the total cost of open facilities and established connections. In a series of recent papers F T F P was essentially reduced to F T F L and then to U F L showing it could be approximated with ratio 1.575. In this paper we show that F T F P can actually be approximated even better. We consider approximation ratio as a function of r = minj∈C rj (minimum requirement of a client). With increasing r the approximation ratio of our algorithm λr converges to one. Furthermore, for r > 1 the value of λr is less than 1.463 (hardness of approximation of U F L). We also show a lower bound of 1.278 for the approximability of the Fault-Tolerant Facility Location problem (F T F L) for arbitrary r. Already for r > 3 we obtain that F T F P can be approximated with ratio 1.275, showing that under standard complexity theoretic assumptions F T F P is strictly better approximable than F T F L.

Improved approximation algorithms for constrained fault-tolerant resource allocation

“…They first gave a 3.16-approximation LP-rounding algorithm [5], and then obtained the ratio of 1.575 [20] built on the work of [12,13,21,19]. Recently, Rybicki and Byrka [22] gave an elegant asymptotic approximation algorithm (with various better ratios depending on min j r j ) and some improved hardness results. For FTRA, the preliminary result is a pseudo-polynomial time 1.52-approximation algorithm [1] for the uniform case.…”