e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
Analysis of a local search heuristic for facility location problems
Journal of Algorithms
Approximation algorithms
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-median problem
Journal of Computer and System Sciences - STOC 1999
Fault-tolerant facility location
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
SIAM Journal on Computing
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
SIAM Journal on Computing
Local Search Heuristics for k-Median and Facility Location Problems
SIAM Journal on Computing
Improved Combinatorial Algorithms for Facility Location Problems
SIAM Journal on Computing
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
The Fault-Tolerant Facility Allocation Problem
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximation algorithms for the Fault-Tolerant Facility Placement problem
Information Processing Letters
The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms
INFORMS Journal on Computing
Unconstrained and constrained fault-tolerant resource allocation
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Improved approximation algorithms for the robust fault-tolerant facility location problem
Information Processing Letters
Fault-tolerant facility location: a randomized dependent LP-Rounding algorithm
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Approximating the reliable resource allocation problem using inverse dual fitting
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Improved approximation algorithms for constrained fault-tolerant resource allocation
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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We consider a fault-tolerant generalization of the classical uncapacitated facility location problem, where each client j has a requirement that rj distinct facilities serve it, instead of just one. We give a 2.076-approximation algorithm for this problem using LP rounding, which is currently the best-known performance guarantee. Our algorithm exploits primal and dual complementary slackness conditions and is based on clustered randomized rounding. A technical difficulty that we overcome is the presence of terms with negative coefficients in the dual objective function, which makes it difficult to bound the cost in terms of dual variables. For the case where all requirements are the same, we give a primal-dual 1.52-approximation algorithm. We also consider a fault-tolerant version of the k-median problem. In the metric k-median problem, we are given n points in a metric space. We must select k of these to be centers, and then assign each input point j to the selected center that is closest to it. In the fault-tolerant version we want j to be assigned to rj distinct centers. The goal is to select the k centers so as to minimize the sum of assignment costs. The primal-dual algorithm for fault-tolerant facility location with uniform requirements also yields a 4-approximation algorithm for the fault-tolerant k-median problem for this case. This the first constant-factor approximation algorithm for the uniform requirements case.