Parameterized graph cleaning problems

Marx, Dániel; Schlotter, Ildikó

doi:10.1016/j.dam.2009.06.022

Cited by 4 publications

(1 citation statement)

References 21 publications

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“…Motivation Many vertex deletion problems in graphs can be considered as "graph cleaning procedures", see Diaz and Thilikos [8] or Marx and Schlotter [21]. This view particularly applies to graph-based data clustering, where the graph vertices represent data items and there is an edge between two vertices if and only if the corresponding items are similar enough [28,30].…”

Section: Introductionmentioning

confidence: 99%

Approximation and Tidying—A Problem Kernel for s-Plex Cluster Vertex Deletion

Bevern¹,

Moser²,

Niedermeier³

2011

Algorithmica

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We introduce the NP-hard graph-based data clustering problem s-PLEX CLUSTER VERTEX DELETION, where the task is to delete at most k vertices from a graph so that the connected components of the resulting graph are s-plexes. In an splex, every vertex has an edge to all but at most s−1 other vertices; cliques are 1-plexes. We propose a new method based on "approximation and tidying" for kernelizing vertex deletion problems whose goal graphs can be characterized by forbidden induced subgraphs. The method exploits polynomial-time approximation results and thus provides a useful link between approximation and kernelization. Employing "approximation and tidying", we develop data reduction rules that, in O(ksn 2 ) time, transform an s-PLEX CLUSTER VERTEX DELETION instance with n vertices into an equivalent instance with O(k 2 s 3 ) vertices, yielding a problem kernel. To this end, we also show how to exploit structural properties of the specific problem in order to significantly improve the running time of the proposed kernelization method.

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Section: Introductionmentioning

confidence: 99%

Approximation and Tidying—A Problem Kernel for s-Plex Cluster Vertex Deletion

Bevern¹,

Moser²,

Niedermeier³

2011

Algorithmica

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Kernelization through Tidying

Bevern

Moser

Niedermeier

2010

LATIN 2010: Theoretical Informatics

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Cleaning Interval Graphs

Marx

Schlotter

2011

Algorithmica

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Abstract. We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard parameterization, where the parameter is the difference |V (G)| − |V (H)|, with G and H being the larger and the smaller input graph, respectively. Intuitively, we can interpret this problem as "cleaning" the graph G, regarded as a pattern containing extra vertices indicating errors, in order to obtain the graph H representing the original pattern. We also prove W[1]-hardness for the standard parameterization where the parameter is |V (H)|.

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Parameterized graph cleaning problems

Cited by 4 publications

References 21 publications

Approximation and Tidying—A Problem Kernel for s-Plex Cluster Vertex Deletion

Approximation and Tidying—A Problem Kernel for s-Plex Cluster Vertex Deletion

Kernelization through Tidying

Cleaning Interval Graphs

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