Approximation algorithms for geometric median problems
Information Processing Letters
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete 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
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
An Iterative Rounding 2-Approximation Algorithm for the Element Connectivity Problem
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Local Search Heuristics for k-Median and Facility Location Problems
SIAM Journal on Computing
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Improved Combinatorial Algorithms for Facility Location Problems
SIAM Journal on Computing
Survivable network design with degree or order constraints
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A simple combinatorial algorithm for submodular function minimization
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Budgeted red-blue median and its generalizations
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Locating depots for capacitated vehicle routing
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Constant factor approximation algorithm for the knapsack median problem
Proceedings of the twenty-third 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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In the classical k-median problem, we are given a metric space and would like to open k centers so as to minimize the sum (over all the vertices) of the distance of each vertex to its nearest open center. In this paper, we consider the following generalization of the problem: instead of opening at most k centers, what if each center belongs to one of T different types, and we are allowed to open at most ki centers of type i (for each i=1,2,...,T). The case T = 1 is the classical k-median, and the case of T = 2 is the red-blue median problem for which Hajiaghayi et al. [ESA 2010] recently gave a constant-factor approximation algorithm. Even more generally, what if the set of open centers had to form an independent set from a matroid? In this paper, we give a constant factor approximation algorithm for such matroid median problems. Our algorithm is based on rounding a natural LP relaxation in two stages: in the first step, we sparsify the structure of the fractional solution while increasing the objective function value by only a constant factor. This enables us to write another LP in the second phase, for which the sparsified LP solution is feasible. We then show that this second phase LP is in fact integral; the integrality proof is based on a connection to matroid intersection. We also consider the penalty version (alternately, the so-called prize collecting version) of the matroid median problem and obtain a constant factor approximation algorithm for it. Finally, we look at the Knapsack Median problem (in which the facilities have costs and the set of open facilities need to fit into a Knapsack) and get a bicriteria approximation algorithm which violates the Knapsack bound by a small additive amount.