Article

The Planar k-Means Problem is NP-Hard

Authors:

Prajakta Nimbhorkar,

Kasturi VaradarajanAuthors Info & Claims

WALCOM '09: Proceedings of the 3rd International Workshop on Algorithms and Computation

Pages 274 - 285

https://doi.org/10.1007/978-3-642-00202-1_24

Published: 18 February 2009 Publication History

Abstract

In the k-means problem, we are given a finite set S of points in $\Re^m$, and integer k ≥ 1, and we want to find k points (centers) so as to minimize the sum of the square of the Euclidean distance of each point in S to its nearest center. We show that this well-known problem is NP-hard even for instances in the plane, answering an open question posed by Dasgupta [6].

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Cited By

Bamas ENagarajan SSvensson OSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Analyzing Dα seeding for k-meansProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692177(2673-2699)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692177
Romanuke V(2023)Speedup of the k-Means Algorithm for Partitioning Large Datasets of Flat Points by a Preliminary Partition and Selecting Initial CentroidsApplied Computer Systems10.2478/acss-2023-000128:1(1-12)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.2478/acss-2023-0001
Schubert E(2023)Stop using the elbow criterion for k-means and how to choose the number of clusters insteadACM SIGKDD Explorations Newsletter10.1145/3606274.360627825:1(36-42)Online publication date: 5-Jul-2023
https://dl.acm.org/doi/10.1145/3606274.3606278
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The Planar k-Means Problem is NP-Hard
1. Theory of computation

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Published In

cover image Guide Proceedings

WALCOM '09: Proceedings of the 3rd International Workshop on Algorithms and Computation

February 2009

405 pages

ISBN:9783642002014

Editors:
Sandip Das
Indian Statistical Institute, Kolkata, India 700 108
,
Ryuhei Uehara
Japan Advanced Institute of Science and Technology, Ishikawa, Japan 923-1292

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 18 February 2009

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Cited By

Bamas ENagarajan SSvensson OSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Analyzing Dα seeding for k-meansProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692177(2673-2699)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692177
Romanuke V(2023)Speedup of the k-Means Algorithm for Partitioning Large Datasets of Flat Points by a Preliminary Partition and Selecting Initial CentroidsApplied Computer Systems10.2478/acss-2023-000128:1(1-12)Online publication date: 1-Jun-2023
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Schubert E(2023)Stop using the elbow criterion for k-means and how to choose the number of clusters insteadACM SIGKDD Explorations Newsletter10.1145/3606274.360627825:1(36-42)Online publication date: 5-Jul-2023
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Choo DGrunau CPortmann JRozhoň VDaumé HSingh A(2020)k-means++Proceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525116(1909-1917)Online publication date: 13-Jul-2020
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