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The Correlation Clustering Problem (CorCP) is a significant clustering problem based on the similarity of data. It has significant applications in different fields, such as machine learning, biology, and data mining, and many different problems in other areas. In this paper, the Balanced $2$-CorCP (B $2$-CorCP) is introduced and examined, and a new interesting variant of the CorCP is described. The goal of this clustering problem is to partition the vertex set into two clusters with equal size, such that the number of disagreements is minimized. We first present a polynomial time algorithm for the B $2$-CorCP on $M$-positive edge dominant graphs $(M⩾3)$. Then, we provide a series of numerical experiments, and the results show the effectiveness of our algorithm.

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# Approximation Algorithm for the Balanced 2-Correlation Clustering Problem

Show Author's information Donglei Du( )Ling Gai( )Zhongrui Zhao
Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing 100124, China
Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China
Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China

## Abstract

The Correlation Clustering Problem (CorCP) is a significant clustering problem based on the similarity of data. It has significant applications in different fields, such as machine learning, biology, and data mining, and many different problems in other areas. In this paper, the Balanced $2$-CorCP (B $2$-CorCP) is introduced and examined, and a new interesting variant of the CorCP is described. The goal of this clustering problem is to partition the vertex set into two clusters with equal size, such that the number of disagreements is minimized. We first present a polynomial time algorithm for the B $2$-CorCP on $M$-positive edge dominant graphs $(M⩾3)$. Then, we provide a series of numerical experiments, and the results show the effectiveness of our algorithm.

## Keywords:

balanced clustering, k-correlation clustering, positive edge dominant graphs, approximation algorithm
Received: 13 February 2021 Revised: 27 May 2021 Accepted: 28 June 2021 Published: 17 March 2022 Issue date: October 2022
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Publication history
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## Publication history

Revised: 27 May 2021
Accepted: 28 June 2021
Published: 17 March 2022
Issue date: October 2022