Isolation Concepts for Enumerating Dense Subgraphs

Komusiewicz, Christian; Hüffner, Falk; Moser, Hannes; Niedermeier, Rolf

doi:10.1007/978-3-540-73545-8_16

Cited by 9 publications

(34 citation statements)

References 12 publications

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“…The s-plex concept was introduced in 1978 by Seidman and Foster [13] in the context of social network analysis. Recently, a number of theoretical and experimental studies explored (and confirmed) the usefulness of s-plexes in various contexts [1,6,10,11]. Finding maximum-cardinality s-plexes is NP-hard [1] and further hardness results in analogy to clique finding hold as well [10].…”

Section: S-plex Editingmentioning

confidence: 99%

A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing

Guo

Komusiewicz

Niedermeier

et al. 2009

Algorithmic Aspects in Information and Management

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Abstract. We introduce the s-Plex Editing problem generalizing the well-studied Cluster Editing problem, both being NP-hard and both being motivated by graph-based data clustering. Instead of transforming a given graph by a minimum number of edge modifications into a disjoint union of cliques (Cluster Editing), the task in the case of s-Plex Editing is now to transform a graph into a disjoint union of so-called s-plexes. Herein, an s-plex denotes a vertex set inducing a (sub)graph where every vertex has edges to all but at most s vertices in the splex. Cliques are 1-plexes. The advantage of s-plexes for s ≥ 2 is that they allow to model a more relaxed cluster notion (s-plexes instead of cliques), which better reflects inaccuracies of the input data. We develop a provably efficient and effective preprocessing based on data reduction (yielding a so-called problem kernel), a forbidden subgraph characterization of s-plex cluster graphs, and a depth-bounded search tree which is used to find optimal edge modification sets. Altogether, this yields efficient algorithms in case of moderate numbers of edge modifications.

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Section: S-plex Editingmentioning

confidence: 99%

A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing

Guo

Komusiewicz

Niedermeier

et al. 2009

Algorithmic Aspects in Information and Management

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“…The fundamental strategy and several basic ideas go back to Ito et al [10]; while their work contains serious flaws as spotted in [12], it initiated the study of isolation in context with the enumeration of maximal cliques. Besides sketching the fundamental algorithmic ideas, we additionally describe a new theoretical result leading to an improved running time.…”

Section: Fundamentals and Algorithms And Implementation Issuesmentioning

confidence: 99%

“…Ito et al [10] introduced the concept of c-isolation-which, in the light of the following is called average-c-isolation (avg-c-isolation for short) in this work-as follows: Let G = (V, E) be an undirected graph and c be a positive integer. A vertex subset S ⊆ V of size k is called avg-c-isolated if it has less than c·k outgoing edges, where an outgoing edge is an edge between a vertex in S and a vertex in V \ S. In follow up-work, we further introduced the concepts of min-c-isolation and max-c-isolation as follows [12]. A vertex set S ⊆ V is minc-isolated if there is at least one vertex in S with less than c neighbors in V \S.…”

Section: Fundamentals and Algorithms And Implementation Issuesmentioning

confidence: 99%

“…This can result in the enumeration of smaller cliques than in the other two cases. The theoretical study [12] of these three concepts led to the following theorem. Herein, n denotes the number of graph vertices and m the number of edges.…”

Section: Fundamentals and Algorithms And Implementation Issuesmentioning

confidence: 99%

“…Unfortunately, their algorithm is flawed. Hence, in our recent theoretical work [12], we presented a nontrivially repaired algorithm with the same running time. Moreover, we introduced two closely related isolation concepts called minc-isolation and max-c-isolation, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Enumerating Isolated Cliques in Synthetic and Financial Networks

Hüffner

Komusiewicz

Moser

et al.

Combinatorial Optimization and Applications

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Abstract. We do computational studies concerning the enumeration of maximal isolated cliques in graphs. Isolation, as recently introduced, measures the degree of connectedness of the cliques to the rest of the graph. Isolation helps both in getting faster algorithms than for the enumeration of maximal general cliques and in filtering out cliques with special semantics. We perform experiments with synthetic graphs (in the Gn,m,p model) and financial networks, proposing the enumeration of isolated cliques as a useful instrument in analyzing financial networks.

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