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The $k$-center problem is a classical combinatorial optimization problem which asks to find $k$ centers such that the maximum distance of any input point in a set $P$ to its assigned center is minimized.
On representatives of subsets
P. Hall · 1935
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Easy and hard bottleneck location problems
Wen-Lian Hsu and George L. Nemhauser · 1979
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Clustering to minimize the maximum intercluster distance
Teofilo F. Gonzalez · 1985
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A unified approach to approximation algorithms for bottleneck problems
Dorit S. Hochbaum and David B. Shmoys · 1986
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How to allocate network centers
Judit Bar-Ilan, Guy Kortsarz, and David Peleg · 1993
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Approximation algorithms for facility location problems
David B. Shmoys, Éva Tardos, and Karen Aardal · 1997
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Greedy strikes back: Improved facility location algorithms
Sudipto Guha and Samir Khuller · 1999
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Fault tolerant k-center problems
Samir Khuller, Robert Pless, and Yoram J. Sussmann · 2000
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The capacitated K -center problem
Samir Khuller and Yoram J. Sussmann · 2000
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Analysis of a local search heuristic for facility location problems
Madhukar R. Korupolu, C. Greg Plaxton, and Rajmohan Rajaraman · 2000
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Algorithms for facility location problems with outliers
Moses Charikar, Samir Khuller, David M. Mount, and Giri Narasimhan · 2001
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Approximation algorithms for metric facility location and k -median problems using the primal-dual schema and lagrangian relaxation
Kamal Jain and Vijay V. Vazirani · 2001
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Constrained k-means clustering with background knowledge
Kiri Wagstaff, Claire Cardie, Seth Rogers, and Stefan Schrödl · 2001
Cited alongside, same era.
A constant-factor approximation algorithm for the k-median problem
Moses Charikar, Sudipto Guha, Éva Tardos, and David B. Shmoys · 2002
Cited alongside, same era.
A new greedy approach for facility location problems
Kamal Jain, Mohammad Mahdian, and Amin Saberi · 2002
Cited alongside, same era.
Local search heuristics for k-median and facility location problems
Vijay Arya, Naveen Garg, Rohit Khandekar, Adam Meyerson, Kamesh Munagala, and Vinayaka Pandit · 2004
Cited alongside, same era.
Achieving anonymity via clustering
Gagan Aggarwal, Rina Panigrahy, Tomás Feder, Dilys Thomas, Krishnaram Kenthapadi, Samir Khuller, and An Zhu · 2010
Cited alongside, same era.
Clustering with diversity
Jian Li, Ke Yi, and Qin Zhang · 2010
Cited alongside, same era.
Constant factor approximation for capacitated k-center with outliers
Marek Cygan and Tomasz Kociumaka · 2014
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Centrality of trees for capacitated k-center
Hyung-Chan An, Aditya Bhaskara, Chandra Chekuri, Shalmoli Gupta, Vivek Madan, and Ola Svensson · 2015
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A unified framework for clustering constrained data without locality property
Hu Ding and Jinhui Xu · 2015
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Approximation algorithms for clustering problems with lower bounds and outliers
Sara Ahmadian and Chaitanya Swamy · 2016
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The non-uniform k k -center problem
Deeparnab Chakrabarty, Prachi Goyal, and Ravishankar Krishnaswamy · 2016
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Matroid and knapsack center problems
Danny Z. Chen, Jian Li, Hongyu Liang, and Haitao Wang · 2016
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Solving the chromatic cone clustering problem via minimum spanning sphere
Hu Ding and Jinhui Xu · 2011
Cited alongside, same era.
A 5-approximation for capacitated facility location
Manisha Bansal, Naveen Garg, and Neelima Gupta · 2012
Cited alongside, same era.
LP rounding for k-centers with non-uniform hard capacities
Marek Cygan, MohammadTaghi Hajiaghayi, and Samir Khuller · 2012
Cited alongside, same era.
A 3-approximation algorithm for the facility location problem with uniform capacities
Ankit Aggarwal, Anand Louis, Manisha Bansal, Naveen Garg, Neelima Gupta, Shubham Gupta, and Surabhi Jain · 2013
Cited alongside, same era.
A 1.488 approximation algorithm for the uncapacitated facility location problem
Shi Li · 2013
Cited alongside, same era.
Approximating connected facility location with lower and upper bounds via LP rounding
Zachary Friggstad, Mohsen Rezapour, and Mohammad R. Salavatipour · 2016
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Approximating k-median via pseudo-approximation
Shi Li and Ola Svensson · 2016
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An improved approximation for k -median and positive correlation in budgeted optimization
Jaroslaw Byrka, Thomas Pensyl, Bartosz Rybicki, Aravind Srinivasan, and Khoa Trinh · 2017
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Fair clustering through fairlets
Flavio Chierichetti, Ravi Kumar, Silvio Lattanzi, and Sergei Vassilvitskii · 2017
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Capacitated center problems with two-sided bounds and outliers
Hu Ding, Lunjia Hu, Lingxiao Huang, and Jian Li · 2017
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