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Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem.
ε \varepsilon -approximations with minimum packing constraint violation (extended abstract)
J.-H. Lin and J. S. Vitter · 1992
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Rounding via trees: Deterministic approximation algorithms for group steiner trees and k -median
M. Charikar, C. Chekuri, A. Goel, and S. Guha · 1998
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Approximating a finite metric by a small number of tree metrics
M. Charikar, C. Chekuri, A. Goel, S. Guha, and S. A. Plotkin · 1998
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A constant-factor approximation algorithm for the k-median problem
M. Charikar, S. Guha, É. Tardos, and D. B. Shmoys · 1999
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Analysis of a local search heuristic for facility location problems
M. R. Korupolu, C. G. Plaxton, and R. Rajaraman · 2000
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A tight bound on approximating arbitrary metrics by tree metrics
J. Fakcharoenphol, S. Rao, and K. Talwar · 2003
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Combinatorial Optimization - Polyhedra and Efficiency
A. Schrijver · 2003
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Local search heuristics for k-median and facility location problems
V. Arya, N. Garg, R. Khandekar, A. Meyerson, K. Munagala, and V. Pandit · 2004
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Approximating k-median with non-uniform capacities
J. Chuzhoy and Y. Rabani · 2005
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Lp rounding for k-centers with non-uniform hard capacities
M. Cygan, M. Hajiaghayi, and S. Khuller · 2012
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Planar f-deletion: Approximation, kernelization and optimal fpt algorithms
F. V. Fomin, D. Lokshtanov, N. Misra, and S. Saurabh · 2012
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Approximating k-median via pseudo-approximation
S. Li and O. Svensson · 2013
Cited alongside, same era.
Approximation algorithms for hard capacitated k-facility location problems
K. Aardal, P. L. van den Berg, D. Gijswijt, and S. Li · 2015
Cited alongside, same era.
Bi-factor approximation algorithms for hard capacitated k-median problems
J. Byrka, K. Fleszar, B. Rybicki, and J. Spoerhase · 2015
Cited alongside, same era.
An approximation algorithm for uniform capacitated k-median problem with 1 + ϵ 1+\epsilon capacity violation
J. Byrka, B. Rybicki, and S. Uniyal · 2016
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Constant approximation for capacitated k-median with ( 1 + ϵ ) (1+\epsilon) -capacity violation
H. G. Demirci and S. Li · 2016
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Approximating capacitated k k -median with ( 1 + ϵ ) k (1+\epsilon)k open facilities
S. Li · 2016
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From gap-eth to fpt-inapproximability: Clique, dominating set, and more
P. Chalermsook, M. Cygan, G. Kortsarz, B. Laekhanukit, P. Manurangsi, D. Nanongkai, and L. Trevisan · 2017
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Partitioning a graph into small pieces with applications to path transversal
E. Lee · 2017
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An fpt algorithm beating 2-approximation for k-cut
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An improved approximation for k-median, and positive correlation in budgeted optimization
J. Byrka, T. Pensyl, B. Rybicki, A. Srinivasan, and K. Trinh · 2015
Cited alongside, same era.
On uniform capacitated k k -median beyond the natural LP
S. Li · 2015
Cited alongside, same era.
A. Gupta, E. Lee, and J. Li · 2018
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Losing treewidth by separating subsets
A. Gupta, E. Lee, J. Li, P. Manurangsi, and M. Wlodarczyk · 2018
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On the parameterized complexity of approximating dominating set
K. C. S., B. Laekhanukit, and P. Manurangsi · 2018
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