Approximation algorithms for geometric median problems
Information Processing Letters
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
K-medians, facility location, and the Chernoff-Wald bound
SODA '00 Proceedings of the eleventh 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
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
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
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
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
Constant factor approximation algorithm for the knapsack median problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A new approximation algorithm for the k-facility location problem
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fault-tolerant facility location: a randomized dependent LP-Rounding algorithm
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Matroid and knapsack center problems
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
| Hi-index | 0.00 |
In this paper, we revisit the classical k-median problem. Using the standard LP relaxation for k-median, we give an efficient algorithm to construct a probability distribution on sets of k centers that matches the marginals specified by the optimal LP solution. Analyzing the approximation ratio of our algorithm presents significant technical difficulties: we are able to show an upper bound of 3.25. While this is worse than the current best known 3+ε guarantee of [2], because: (1) it leads to 3.25 approximation algorithms for some generalizations of the k-median problem, including the k-facility location problem introduced in [10], (2) our algorithm runs in $\tilde{O}(k^3 n^2/\delta^2)$ time to achieve 3.25(1+δ)-approximation compared to the O(n8) time required by the local search algorithm of [2] to guarantee a 3.25 approximation, and (3) our approach has the potential to beat the decade old bound of 3+ε for k-median. We also give a 34-approximation for the knapsack median problem, which greatly improves the approximation constant in [13]. Using the same technique, we also give a 9-approximation for matroid median problem introduced in [11], improving on their 16-approximation.