Graph-based data clustering with overlaps

Fellows, Michael R.; Guo, Jiong; Komusiewicz, Christian; Niedermeier, Rolf; Uhlmann, Johannes

doi:10.1016/j.disopt.2010.09.006

Cited by 62 publications

(24 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This clustering can be obtained by modifying the input graph for example by deleting edges so that all remaining edges are only inside clusters. Starting with Cluster Editing [19], there are by now numerous parameterized algorithmics studies on graph modification problems related to clustering, varying on the cluster graph definition [4,11,14,20,32], the modification operation [28], or both [3]. Most of the examples of variants of Cluster Editing evolved primarily from a graph-theoretic interest.…”

Section: From Heuristics To Parameterized Problemsmentioning

confidence: 99%

Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics

Komusiewicz

Nichterlein

Niedermeier

2016

Graph-Theoretic Concepts in Computer Science

Self Cite

View full text Add to dashboard Cite

In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster Deletion problem asks to delete as few edges as possible such that the resulting graph is a disjoint union of cliques. Graph modification problems appear in numerous applications, including the analysis of biological and social networks. Typically, graph modification problems are NP-hard, making them natural candidates for parameterized complexity studies. We discuss several fruitful interactions between the development of fixed-parameter algorithms and the design of heuristics for graph modification problems, featuring quite different aspects of mutual benefits.

show abstract

Section: From Heuristics To Parameterized Problemsmentioning

confidence: 99%

Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics

Komusiewicz

Nichterlein

Niedermeier

2016

Graph-Theoretic Concepts in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…The most natural candidates appear to be problems where the forbidden induced subgraph has four vertices. Examples are Cograph Editing [35] which is the problem of destroying all induced P 4 s, K 4 -free Editing, Claw-free Editing, and Diamond-free Deletion [18,44]. Another direction could be to investigate edge completion problems that allow for subexponential-time algorithms [15].…”

Section: Resultsmentioning

confidence: 99%

Parameterizing Edge Modification Problems Above Lower Bounds

2017

Self Cite

View full text Add to dashboard Cite

We study the parameterized complexity of a variant of the F -FREE EDIT-ING problem: Given a graph G and a natural number k, is it possible to modify at most k edges in G so that the resulting graph contains no induced subgraph isomorphic to F ? In our variant, the input additionally contains a vertex-disjoint packing H of induced subgraphs of G, which provides a lower bound h(H) on the number of edge modifications required to transform G into an F -free graph. While earlier works used the number k as parameter or structural parameters of the input graph G, we consider instead the parameter := k − h(H), that is, the number of edge modifications above the lower bound h(H). We develop a framework of generic data reduction An extended abstract of this article appeared in Theory Comput Syst rules to show fixed-parameter tractability with respect to for K 3 -FREE EDITING, FEEDBACK ARC SET IN TOURNAMENTS, and CLUSTER EDITING when the packing H contains subgraphs with bounded solution size. For K 3 -FREE EDITING, we also prove NP-hardness in case of edge-disjoint packings of K 3 s and = 0, while for K q -FREE EDITING and q ≥ 6, NP-hardness for = 0 even holds for vertex-disjoint packings of K q s. In addition, we provide NP-hardness results for F -FREE VERTEX DELETION, were the aim is to delete a minimum number of vertices to make the input graph F -free.

show abstract

“…[7]). See [13] for a recent review, with several complexity results. The extensive literature on FPT algorithms for solving the Cluster editing problem apparently does not extend in the same degree to polynomial time solvable cases.…”

Section: Introductionmentioning

confidence: 98%