P-Complete Approximation Problems
Journal of the ACM (JACM)
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Relations between average case complexity and approximation complexity
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
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Improved Combinatorial Algorithms for Facility Location Problems
SIAM Journal on Computing
Approximating k-median with non-uniform capacities
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
How to Pay, Come What May: Approximation Algorithms for Demand-Robust Covering Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The reverse greedy algorithm for the metric k-median problem
Information Processing Letters
Prediction, Learning, and Games
Prediction, Learning, and Games
Dependent rounding and its applications to approximation algorithms
Journal of the ACM (JACM)
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
Robust Combinatorial Optimization with Exponential Scenarios
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Sampling bounds for stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Operations Research Letters
Exceeding expectations and clustering uncertain data
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Large-scale uncertainty management systems: learning and exploiting your data
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
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This paper studies an extension of the k-median problem where we are given a metric space (V, d) and not just one but m client sets {Si ⊆ V}im=1, and the goal is to open k facilities F to minimize: maxi∈[m] {Σj∈Si d(j, F)}, i.e., the worst-case cost over all the client sets. This is a "min-max" or "robust" version of the k-median problem; however, note that in contrast to previous papers on robust/stochastic problems, we have only one stage of decision-making---where should we place the facilities? We present an O(log n + log m) approximation for robust k-median: The algorithm is combinatorial and very simple, and is based on reweighting/Lagrangean-relaxation ideas. In fact, we give a general framework for (minimization) facility location problems where there is a bound on the number of open facilities. For robust and stochastic versions of such location problems, we show that if the problem satisfies a certain "projection" property, essentially the same algorithm gives a logarithmic approximation ratio in both versions. We use our framework to give the first approximation algorithms for robust/stochastic versions of k-tree, capacitated k-median, and fault-tolerant k-median.