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The k-means problem consists of finding k centers in the d-dimensional Euclidean space that minimize the sum of the squared distances of all points in an input set P to their closest respective center.
Stuart P. Lloyd, Least squares quantization in PCM , Bell Laboratories Technical Memorandum (1957), later published as [ Llo82 ]
1957
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Mary Inaba, Naoki Katoh, and Hiroshi Imai, Applications of weighted voronoi diagrams and randomization to variance-based k-clustering (extended abstract) , Proceedings of the 10th ACM Symposium on Computational Geometry (SoCG, 1994, pp. 332–339
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Kamal Jain and Vijay V. Vazirani, Approximation algorithms for metric facility location and k k -median problems using the primal-dual schema and lagrangian relaxation , Journal of the ACM 48
2001
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Tapas Kanungo, David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman, and Angela Y. Wu, A local search approximation algorithm for k k -means clustering , Computational Geometry 28
2004
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Irit Dinur and Samuel Safra, On the hardness of approximating minimum vertex cover , Annals of Mathematics (2005), 439–485
2005
Cited alongside, same era.
2005
Cited alongside, same era.
Miroslav Chlebík and Janka Chlebíková, Complexity of approximating bounded variants of optimization problems , Theoretical Computer Science 354
2006
Cited alongside, same era.
Sanjoy Dasgupta, The hardness of k k -means clustering , Tech. Report CS2008-0916, University of California, 2008
2008
Cited alongside, same era.
Daniel Aloise, Amit Deshpande, Pierre Hansen, and Preyas Popat, NP-hardness of Euclidean sum-of-squares clustering , Machine Learning 75
2009
Later among the works it cites.
Meena Mahajan, Prajakta Nimbhorkar, and Kasturi R. Varadarajan, The Planar k k -means Problem is NP-Hard , Proceedings of the 3rd Workshop on Algorithms and Computation (WALCOM), 2009, pp. 274 – 285
2009
Later among the works it cites.
Dan Feldman and Michael Langberg, A unified framework for approximating and clustering data , Proceedings of the 43th ACM Symposium on the Theory of Computing (STOC), 2011, pp. 569 – 578
2011
Later among the works it cites.
Pranjal Awasthi, Moses Charikar, Ravishankar Krishnaswamy, and Ali Kemal Sinop, The hardness of approximation of euclidean k-means , SoCG 2015 (accepted), 2015
2015
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