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In this paper, we present a new iterative rounding framework for many clustering problems.
Approximation algorithms for facility location problems (extended abstract)
David B. Shmoys, Éva Tardos, and Karen Aardal · 1997
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Approximation schemes for euclidean k-medians and related problems
Sanjeev Arora, Prabhakar Raghavan, and Satish Rao · 1998
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Greedy strikes back: Improved facility location algorithms
Sudipto Guha and Samir Khuller · 1998
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Analysis of a local search heuristic for facility location problems
Madhukar R. Korupolu, C. Greg Plaxton, and Rajmohan Rajaraman · 1998
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A constant-factor approximation algorithm for the k-median problem
M. Charikar, S. Guha, D. Shmoys, and E. Tardos · 1999
Earlier work this paper cites.
Improved combinatorial algorithms for the facility location and k-median problems
Moses Charikar and Sudipto Guha · 1999
Earlier work this paper cites.
Local search heuristic for k-median and facility location problems
Vijay Arya, Naveen Garg, Rohit Khandekar, Adam Meyerson, Kamesh Munagala, and Vinayaka Pandit · 2001
Earlier work this paper cites.
Algorithms for facility location problems with outliers
M. Charikar, S. Khuller, D. M. Mount, and G. Narasimhan · 2001
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Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation
K. Jain and V. V. Vazirani · 2001
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A new greedy approach for facility location problems
Kamal Jain, Mohammad Mahdian, and Amin Saberi · 2002
Earlier work this paper cites.
Improved approximation algorithms for the uncapacitated facility location problem
Fabián A. Chudak and David B. Shmoys · 2003
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Greedy facility location algorithms analyzed using dual fitting with factor-revealing lp
Kamal Jain, Mohammad Mahdian, Evangelos Markakis, Amin Saberi, and Vijay V. Vazirani · 2003
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Least squares quantization in pcm
S. Lloyd · 2006
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Approximation algorithms for metric facility location problems
Mohammad Mahdian, Yinyu Ye, and Jiawei Zhang · 2006
Earlier work this paper cites.
K-means++: The advantages of careful seeding
David Arthur and Sergei Vassilvitskii · 2007
Cited alongside, same era.
An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem
Jaroslaw Byrka · 2007
Cited alongside, same era.
A constant factor approximation algorithm for k-median clustering with outliers
Ke Chen · 2008
Cited alongside, same era.
Stability yields a PTAS for k-median and k-means clustering
Pranjal Awasthi, Avrim Blum, and Or Sheffet · 2010
Cited alongside, same era.
Clustering with spectral norm and the k-means algorithm
Amit Kumar and Ravindran Kannan · 2010
Cited alongside, same era.
Smoothed analysis of the k-means method
David Arthur, Bodo Manthey, and Heiko Röglin · 2011
Cited alongside, same era.
k-means–: A unified approach to clustering and outlier detection
Sanjay Chawla and Aristides Gionis · 2013
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Approximating k-median via pseudo-approximation
S. Li and O. Svensson · 2013
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On integrated clustering and outlier detection
Lionel Ott, Linsey Pang, Fabio T Ramos, and Sanjay Chawla · 2014
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An improved approximation algorithm for knapsack median using sparsification
Jaroslaw Byrka, Thomas Pensyl, Bartosz Rybicki, Joachim Spoerhase, Aravind Srinivasan, and Khoa Trinh · 2015
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The power of local search for clustering
Vincent Cohen-Addad, Philip N. Klein, and Claire Mathieu · 2016
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The matroid median problem
Ravishankar Krishnaswamy, Amit Kumar, Viswanath Nagarajan, Yogish Sabharwal, and Barna Saha · 2011
Cited alongside, same era.
A 1.488 Approximation Algorithm for the Uncapacitated Facility Location Problem
Shi Li · 2011
Cited alongside, same era.
The Design of Approximation Algorithms
David P. Williamson and David B. Shmoys · 2011
Cited alongside, same era.
A dependent lp-rounding approach for the k-median problem
Moses Charikar and Shi Li · 2012
Cited alongside, same era.
Local search algorithms for the red-blue median problem
M. Hajiaghayi, R. Khandekar, and G. Kortsarz · 2012
Cited alongside, same era.
Constant factor approximation algorithm for the knapsack median problem
Amit Kumar · 2012
Cited alongside, same era.
Zachary Friggstad, Mohsen Rezapour, and Mohammad R. Salavatipour · 2016
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Improved approximation algorithms for matroid and knapsack median problems and applications
Chaitanya Swamy · 2016
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Better guarantees for k-means and euclidean k-median by primal-dual algorithms
Sara Ahmadian, Ashkan Norouzi-Fard, Ola Svensson, and Justin Ward · 2017
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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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On the Local Structure of Stable Clustering Instances
V. Cohen-Addad and C. Schwiegelshohn · 2017
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Local search methods for k-means with outliers
Shalmoli Gupta, Ravi Kumar, Kefu Lu, Benjamin Moseley, and Sergei Vassilvitskii · 2017
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Improved and simplified inapproximability for k-means
Euiwoong Lee, Melanie Schmidt, and John Wright · 2017
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Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization
N. Rujeerapaiboon, K. Schindler, D. Kuhn, and W. Wiesemann · 2017
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Approximation schemes for clustering with outliers
Zachary Friggstad, Kamyar Khodamoradi, Mohsen Rezapour, and Mohammad R. Salavatipour · 2018
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