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The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms.
A linear space algorithm for computing maximal common subsequences
D. S. Hirschberg · 1975
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Efficient dynamic programming using quadrangle inequalities
F. Frances Yao · 1980
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Geometric applications of a matrix-searching algorithm
Alok Aggarwal, Maria M. Klawe, Shlomo Moran, Peter Shor, and Robert Wilber · 1987
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The least weight subsequence problem
D. S. Hirschberg and L. L. Larmore · 1987
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The concave least-weight subsequence problem revisited
Robert Wilber · 1988
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A simple linear time algorithm for concave one-dimensional dynamic programming
Maria M. Klawe · 1989
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Optimal quantization by matrix searching
Xiaolin Wu · 1991
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Finding a minimum-weight-link path in graphs with the concave monge property and applications
A. Aggarwal, B. Schieber, and T. Tokuyama · 1994
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Computing a minimum weight-link path in graphs with the concave monge property
Baruch Schieber · 1998
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Clustering with bregman divergences
Arindam Banerjee, Srujana Merugu, Inderjit S. Dhillon, and Joydeep Ghosh · 2005
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How slow is the k-means method?
David Arthur and Sergei Vassilvitskii · 2006
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k-means++: The advantages of careful seeding
David Arthur and Sergei Vassilvitskii · 2007
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Np-hardness of euclidean sum-of-squares clustering
Daniel Aloise, Amit Deshpande, Pierre Hansen, and Preyas Popat · 2009
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The Planar k-Means Problem is NP-Hard
Meena Mahajan, Prajakta Nimbhorkar, and Kasturi Varadarajan · 2009
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Bregman voronoi diagrams
Jean-Daniel Boissonnat, Frank Nielsen, and Richard Nock · 2010
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Analysis of ego network structure in online social networks
Valerio Arnaboldi, Marco Conti, Andrea Passarella, and Fabio Pezzoni · 2012
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From genome mining to phenotypic microarrays: Planctomycetes as source for novel bioactive molecules
Olga Jeske, Mareike Jogler, Jörn Petersen, Johannes Sikorski, and Christian Jogler · 2013
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Optimal interval clustering: Application to bregman clustering and statistical mixture learning
Frank Nielsen and Richard Nock · 2014
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The retail market as a complex system
Diego Pennacchioli, Michele Coscia, Salvatore Rinzivillo, Fosca Giannotti, and Dino Pedreschi · 2014
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The hardness of approximation of euclidean k-means
Pranjal Awasthi, Moses Charikar, Ravishankar Krishnaswamy, and Ali Kemal Sinop · 2015
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Better guarantees for k-means and euclidean k-median by primal-dual algorithms
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A dynamic programming approach to length-limited huffman coding: space reduction with the monge property
Mordecai J. Golin and Yan Zhang · 2010
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k-means requires exponentially many iterations even in the plane
Andrea Vattani · 2011
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Ckmeans. 1d. dp: optimal k-means clustering in one dimension by dynamic programming
Haizhou Wang and Mingzhou Song · 2011
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Sara Ahmadian, Ashkan Norouzi-Fard, Ola Svensson, and Justin Ward · 2016
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Improved and simplified inapproximability for k-means
Euiwoong Lee, Melanie Schmidt, and John Wright · 2017
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Ckmeans.1d.dp: Optimal and fast univariate clustering; R package version 4.0.0., 2017
Haizhou Wang and Joe Song · 2017
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