Approximation Algorithms on k-Correlation Clustering

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  • 1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China;
    2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China

Received date: 2021-07-13

  Revised date: 2022-02-25

  Online published: 2023-12-26

Supported by

This work was supported by the National Natural Science Foundation of China (Nos. 11901605 and 12101069), the disciplinary funding of Central University of Finance and Economics (CUFE), the Emerging Interdisciplinary Project of CUFE, the Fundamental Research Funds for the Central Universities and Innovation Foundation of BUPT for Youth (No. 500421358).

Abstract

In this paper, we consider the k-correlation clustering problem. Given an edge-weighted graph G(V, E) where the edges are labeled either “+” (similar) or “-” (different) with nonnegative weights, we want to partition the nodes into at most k-clusters to maximize agreements—the total weights of “+” edges within clusters and “-” edges between clusters. This problem is NP-hard. We design an approximation algorithm with the approximation ratio max $\left\{a, \frac{(2-k) a+k-1}{k}\right\}$, where a is the weighted proportion of “+” edges in all edges. As a varies from 0 to 1, the approximation ratio varies from $\frac{k-1}{k}$ to 1 and the minimum value is 1/2.

Cite this article

Zhong-Zheng Tang, Zhuo Diao . Approximation Algorithms on k-Correlation Clustering[J]. Journal of the Operations Research Society of China, 2023 , 11(4) : 911 -924 . DOI: 10.1007/s40305-022-00418-4

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