1-mean and 1-medoid 2-clustering problem with arbitrary cluster sizes: Complexity and approximation-Reference-Cited by-同舟云学术

1-mean and 1-medoid 2-clustering problem with arbitrary cluster sizes: Complexity and approximation

Published:2023 Issue:1 Volume:33 Page:59-69
ISSN:0354-0243
Container-title:Yugoslav Journal of Operations Research
language:en
Short-container-title:YUGOSLAV J OPERATION

Author:

Pyatkin Artem¹

Affiliation:

1. Sobolev Institute of Mathematics, Russia, Novosibirsk + Novosibirsk State University, Russia, Novosibirsk

Abstract

We consider the following 2-clustering problem. Given N points in Euclidean space, partition it into two subsets (clusters) so that the sum of squared distances between the elements of the clusters and their centers would be minimum. The center of the first cluster coincides with its centroid (mean) while the center of the second cluster should be chosen from the set of the initial points (medoid). It is known that this problem is NP-hard if the cardinalities of the clusters are given as a part of the input. In this paper we prove that the problem remains NP-hard in the case of arbitrary clusters sizes and suggest a 2-approximation polynomial-time algorithm for this problem.

Publisher

National Library of Serbia

Subject

Management Science and Operations Research

Reference22 articles.

1. A.V. Pyatkin, “NP-hardness of 1-Mean and 1-Medoid 2-Clustering Problem with Arbitrary Clusters Sizes”, in MOTOR 2021. Communications in Computer and Information Science, vol. 1476, pp. 248-256, 2021.

2. P. Berkhin, “A Survey of Clustering Data Mining Techniques”, in Kogan J., Nicholas C., Teboulle M. (eds) Grouping Multidimensional Data. Springer, Berlin, Heidelberg, 2006.

3. R. C. Dubes, and A. K. Jain, Algorithms for Clustering Data, Prentice Hall, Englewood Cliffs, New Jersey, 07632, 1988.

4. S. Ghoreyshi, and J. Hosseinkhani, “Developing a Clustering Model based on K-Means Algorithm in order to Creating Different Policies for Policyholders”, International Journal of Advanced Computer Science and Information Technology, vol. 4, no. 2, pp. 46-53, 2015.

5. W. D. Fisher, “On Grouping for Maximum Homogeneity”, Journal of the American Statistical Association, vol. 53, no. 284, pp. 789-798, 1958.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. PTAS for Problems of Vector Choice and Clustering with Various Centers;Journal of Applied and Industrial Mathematics;2023-09

2. PTAS for p-Means q-Medoids r-Given Clustering Problem;Mathematical Optimization Theory and Operations Research;2023