Improved Approximation Algorithms for Constrained Fault-Tolerant Resource Allocation
In 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. Each site i can open at most R i facilities with opening cost f i . 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 ∞ )  and the classical Fault-Tolerant Facility Location (FTFL)  problems: for every site i, FTRA ∞ 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 an approximation ratio of 4. Then we show the problem reduces to FTFL, implying the ratio of 1.7245 from . 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.
KeywordsFacility Location Facility Location Problem Open Facility Connection Cost Uncapacitated Facility Location Problem
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