A Fast Branching Algorithm for Cluster Vertex Deletion

In the family of clustering problems we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques). Hüffner et...

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Veröffentlicht in:Theory of computing systems Jg. 58; H. 2; S. 357 - 376
Hauptverfasser: Boral, Anudhyan, Cygan, Marek, Kociumaka, Tomasz, Pilipczuk, Marcin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.02.2016
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Clusters
Compressing
Computer Science
Deletion
Editing
Graph theory
Graphs
Studies
Texts
Theory of Computation
Unions
Branching
Cluster vertex deletion
Fixed-parameter algorithms
ISSN:1432-4350, 1433-0490
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Zusammenfassung:In the family of clustering problems we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques). Hüffner et al. (Theory Comput. Syst. 47 (1), 196–217, 2010 ) initiated the parameterized study of Cluster Vertex Deletion , where the allowed modification is vertex deletion, and presented an elegant 𝓞 min ( 2 k k 6 log k + n 3 , 2 k km n log n ) -time fixed-parameter algorithm, parameterized by the solution size. In the last 5 years, this algorithm remained the fastest known algorithm for Cluster Vertex Deletion and, thanks to its simplicity, became one of the textbook examples of an application of the iterative compression principle. In our work we break the 2 k -barrier for Cluster Vertex Deletion and present an 𝓞 ( 1.910 2 k ( n + m ) ) -time branching algorithm. We achieve this improvement by a number of structural observations which we incorporate into the algorithm’s branching steps.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-015-9631-7