The planar k-means problem is NP-hard

被引：149
|
作者：
Mahajan, Meena [1 ]
Nimbhorkar, Prajakta [1 ]
Varadarajan, Kasturi [2 ]
机构：
[1] Inst Math Sci, Madras 600113, Tamil Nadu, India
[2] Univ Iowa, Iowa City, IA 52242 USA
来源：
THEORETICAL COMPUTER SCIENCE | 2012年 / 442卷
关键词：
Clustering; k-means; Planar graphs; NP-hardness;
D O I：
10.1016/j.tcs.2010.05.034
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In the k-means problem, we are given a finite set S of points in R-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 (2007) [7]. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：13 / 21
页数：9
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