e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth 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
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 constant-factor approximation algorithm for the k-median problem
Journal of Computer and System Sciences - STOC 1999
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 Combinatorial Algorithms for Facility Location Problems
SIAM Journal on Computing
Budgeted red-blue median and its generalizations
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A dependent LP-rounding approach for the k-median problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Matroid and knapsack center problems
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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We give a constant factor approximation algorithm for the following generalization of the k-median problem. We are given a set of clients and facilities in a metric space. Each facility has a facility opening cost, and we are also given a budget B. The objective is to open a subset of facilities of total cost at most B, and minimize the total connection cost of the clients. This settles an open problem of Krishnaswamy-Kumar-Nagarajan-Sabharwal-Saha. The natural linear programming relaxation for this problem has unbounded integrality gap. Our algorithm strengthens this relaxation by adding constraints which stipulate which facilities a client can get assigned to. We show that after suitably modifying a fractional solution, one can get rich structural properties which allow us to get the desired approximation ratio.