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Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems.
Approximation algorithms for geometric median problems
J. Lin and J. S. Vitter · 1992
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Approximation algorithms for facility location problems (extended abstract)
D. B. Shmoys, E. Tardos, and K. Aardal · 1997
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On approximate geometric k-clustering
J. Matoušek · 2000
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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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Approximation Algorithms
V. V. Vazirani · 2001
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A new greedy approach for facility location problems
K. Jain, M. Mahdian, and A. Saberi · 2002
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Lagrangian relaxation for the k-median problem: New insights and continuity properties
A. Archer, R. Rajagopalan, and D. B. Shmoys · 2003
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Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
K. Jain, M. Mahdian, E. Markakis, A. Saberi, and V. V. Vazirani · 2003
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Local search heuristics for k k -median and facility location problems
V. Arya, N. Garg, R. Khandekar, A. Meyerson, K. Munagala, and V. Pandit · 2004
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Improved approximation algorithms for the uncapacitated facility location problem
F. A. Chudak and D. B. Shmoys · 2004
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A local search approximation algorithm for k-means clustering
T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu · 2004
Cited alongside, same era.
Improved combinatorial algorithms for facility location problems
M. Charikar and S. Guha · 2005
Cited alongside, same era.
How slow is the k-means method?
D. Arthur and S. Vassilvitskii · 2006
Cited alongside, same era.
Least squares quantization in PCM
S. Lloyd · 2006
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K-means++: The advantages of careful seeding
D. Arthur and S. Vassilvitskii · 2007
Cited alongside, same era.
A PTAS for k-means clustering based on weak coresets
D. Feldman, M. Monemizadeh, and C. Sohler · 2007
Cited alongside, same era.
k-means requires exponentially many iterations even in the plane
A. Vattani · 2011
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The Design of Approximation Algorithms
D. P. Williamson and D. B. Shmoys · 2011
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A 1.488 approximation algorithm for the uncapacitated facility location problem
S. Li · 2013
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The effectiveness of Lloyd-type methods for the k-means problem
R. Ostrovsky, Y. Rabani, L. J. Schulman, and C. Swamy · 2013
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The hardness of approximation of euclidean k-means
P. Awasthi, M. Charikar, R. Krishnaswamy, and A. K. Sinop · 2015
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An improved approximation for k -median, and positive correlation in budgeted optimization
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A. Gupta and K. Tangwongsan · 2008
Cited alongside, same era.
Approximate clustering without the approximation
M.-F. Balcan, A. Blum, and A. Gupta · 2009
Cited alongside, same era.
Stability yields a PTAS for k-median and k-means clustering
P. Awasthi, A. Blum, and O. Sheffet · 2010
Cited alongside, same era.
An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem
J. Byrka and K. Aardal · 2010
Cited alongside, same era.
J. Byrka, T. Pensyl, B. Rybicki, A. Srinivasan, and K. Trinh · 2015
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Improved and simplified inapproximability for k-means
E. Lee, M. Schmidt, and J. Wright · 2015
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The power of local search for clustering
V. Cohen-Addad, P. N. Klein, and C. Mathieu · 2016
Closest in time.
Local search yields a PTAS for k-means in doubling metrics
Z. Friggstad, M. Rezapour, and M. R. Salavatipour · 2016
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Approximating k-median via pseudo-approximation
S. Li and O. Svensson · 2016
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