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 Ri facilities with opening cost fi. Each client j requires an allocation of rj open facilities and connecting j to any facility at site i incurs a connection cost cij. The goal is to minimize the total cost of this resource allocation scenario. FTRA generalizes the Unconstrained Fault-Tolerant Resource Allocation (FTRA∞) [10] and the classical Fault-Tolerant Facility Location (FTFL) [7] problems: for every site i, FTRA∞ does not have the constraint Ri, whereas FTFL sets Ri=1. These problems are said to be uniform if all rj'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 [2]. For the uniform FTRA, we provide a 1.52-approximation primal-dual algorithm in O(n4) time, where n is the total number of sites and clients.
['Kewen Liao', 'Hong Shen', 'Longkun Guo']
Improved approximation algorithms for constrained fault-tolerant resource allocation