Christian Komusiewicz

Fixed-Parameter Algorithms for Cluster Vertex Deletion

We initiate the first systematic study of the NP-hard Cluster Vertex Deletion (CVD) problem (unweighted and weighted) in terms of fixed-parameter algorithmics. In the unweighted case, one searches for a minimum number of vertex deletions to transform a graph into a collection of disjoint cliques. The parameter is the number of vertex deletions. We present efficient fixed-parameter algorithms for CVD applying the fairly new iterative compression technique. Moreover, we study the variant of CVD where the maximum number of cliques to be generated is prespecified. Here, we exploit connections to fixed-parameter algorithms for (weighted) Vertex Cover.

Parameterized computational complexity of finding small-diameter subgraphs

Finding subgraphs of small diameter in undirected graphs has been seemingly unexplored from a parameterized complexity perspective. We perform the first parameterized complexity study on the corresponding NP-hard s-Club problem. We consider two parameters: the solution size and its dual.

A More Relaxed Model for Graph-Based Data Clustering:

We introduce the

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-Plex Cluster Editing

-Plex Cluster Editing problem as a generalization of the well-studied Cluster Editing problem; both are NP-hard and both are 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 (this is Cluster Editing), the task in the case of

On Generating Triangle-Free Graphs

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Isolation concepts for efficiently enumerating dense subgraphs

-Plex Cluster Editing is to transform a graph into a cluster graph consisting of a disjoint union of so-called

Improved algorithms for bicluster editing

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Measuring indifference: unit interval vertex deletion

-plexes. Herein, an

On Structural Parameterizations for the 2-Club Problem

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