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On Cluster Editing Problem with Clusters of Small Sizes

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN: 1611-3349, Vol: 14395 LNCS, Page: 316-328
2023
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Conference Paper Description

In the cluster editing problem, one has to partition the set of vertices of a graph into disjoint subsets (called clusters) minimizing the number of edges between clusters and the number of missing edges within clusters. We consider a version of the problem in which cluster sizes are bounded from above by a positive integer s. This problem is NP-hard for any fixed s⩾ 3. We propose polynomial-time approximation algorithms for this version of the problem. Their performance guarantees are equal to 5/3 and 5/2 for the cases s= 3 and s= 4, respectively. We also show that the cluster editing problem is APX-complete for the case s= 3 even if the maximum degree of the graphs is bounded by 4.

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