Graph-based data clustering with overlaps

We introduce overlap cluster graph modification problems where, other than in most previous works, the clusters of the target graph may overlap. More precisely, the studied graph problems ask for a minimum number of edge modifications such that the resulting graph consists of clusters (that is, maxi...

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Veröffentlicht in:Discrete optimization Jg. 8; H. 1; S. 2 - 17
Hauptverfasser: Fellows, Michael R., Guo, Jiong, Komusiewicz, Christian, Niedermeier, Rolf, Uhlmann, Johannes
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.02.2011
Schlagworte:
[formula omitted]-hardness
Cluster graph modification problems
Fixed-parameter tractability
Forbidden subgraph characterization
Kernelization
NP-hardness
NP-hardness
Forbidden subgraph characterization
W -hardness
Fixed-parameter tractability
Cluster graph modification problems
Kernelization
ISSN:1572-5286, 1873-636X
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Beschreibung
Zusammenfassung:We introduce overlap cluster graph modification problems where, other than in most previous works, the clusters of the target graph may overlap. More precisely, the studied graph problems ask for a minimum number of edge modifications such that the resulting graph consists of clusters (that is, maximal cliques) that may overlap up to a certain amount specified by the overlap number  s . In the case of s -vertex-overlap, each vertex may be part of at most  s maximal cliques; s -edge-overlap is analogously defined in terms of edges. We provide a complexity dichotomy (polynomial-time solvable versus NP-hard) for the underlying edge modification problems, develop forbidden subgraph characterizations of “cluster graphs with overlaps”, and study the parameterized complexity in terms of the number of allowed edge modifications, achieving fixed-parameter tractability (in case of constant s -values) and parameterized hardness (in case of unbounded s -values).
ISSN:1572-5286
1873-636X
DOI:10.1016/j.disopt.2010.09.006