A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
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 geometric median problems
Information Processing Letters
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Analysis of a local search heuristic for facility location problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Greedy strikes back: improved facility location algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs
SIAM Journal on Optimization
Mathematical Programming for Data Mining: Formulations and Challenges
INFORMS Journal on Computing
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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
Approximating k-median with non-uniform capacities
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Stability Yields a PTAS for k-Median and k-Means Clustering
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A 1.488 approximation algorithm for the uncapacitated facility location problem
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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We present a novel approximation algorithm for k-median that achieves an approximation guarantee of 1+√3+ε, improving upon the decade-old ratio of 3+ε. Our approach is based on two components, each of which, we believe, is of independent interest. First, we show that in order to give an α-approximation algorithm for k-median, it is sufficient to give a pseudo-approximation algorithm that finds an α-approximate solution by opening k+O(1) facilities. This is a rather surprising result as there exist instances for which opening k+1 facilities may lead to a significant smaller cost than if only k facilities were opened. Second, we give such a pseudo-approximation algorithm with α= 1+√3+ε. Prior to our work, it was not even known whether opening k + o(k) facilities would help improve the approximation ratio.