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Making a graph unit interval by a minimum number of vertex deletions is NP-hard. The problem is motivated by applications in seriation and measuring indifference between data items. We present a fixedparameter algorithm based on the iterative compression technique that finds in O((14k + 14)kn) time a set of k vertices whose deletion from an n-vertex graph… (More)

The Bisection problem asks for a partition of the vertices of a graph into two equally sized sets, while minimizing the cut size. This is the number of edges connecting the two vertex sets. Bisection has been thoroughly studied in the past. However, only few results have been published that consider the parameterized complexity of this problem. We show that… (More)

- Nadja Betzler, René van Bevern, Michael R. Fellows, Christian Komusiewicz, Rolf Niedermeier
- IEEE/ACM Transactions on Computational Biology…
- 2011

We study the NP-hard List-Colored Graph Motif problem which, given an undirected list-colored graph G=(V,E) and a multiset M of colors, asks for maximum-cardinality sets S\subseteq V and M^{\prime }\subseteq M such that G[S] is connected and contains exactly (with respect to multiplicity) the colors in M^{\prime }. List-Colored Graph Motif has applications… (More)

- René van Bevern
- Algorithmica
- 2012

A sunflower in a hypergraph is a set of hyperedges pairwise intersecting in exactly the same vertex set. Sunflowers are a useful tool in polynomial-time data reduction for problems formalizable as d-Hitting Set, the problem of covering all hyperedges (whose cardinality is bounded from above by a constant d) of a hypergraph by at most k vertices.… (More)

- René van Bevern, Matthias Mnich, Rolf Niedermeier, Mathias Weller
- J. Scheduling
- 2012

Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent vertices). Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and… (More)

- René van Bevern, Andreas Emil Feldmann, Manuel Sorge, Ondrej Suchý
- Theory of Computing Systems
- 2014

A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equal-sized parts. We prove that Bisection is FPT for the distance to constant cliquewidth if we are given the deletion set. This implies FPT algorithms for… (More)

An author’s profile on Google Scholar consists of indexed articles and associated data, such as the number of citations and the H-index. The author is allowed to merge articles, which may affect the H-index. We analyze the parameterized complexity of maximizing the H-index using article merges. Herein, to model realistic manipulation scenarios, we define a… (More)

Finding a vertex subset in a graph that satisfies a certain property is one of the most-studied topics in algorithmic graph theory. The focus herein is often on minimizing or maximizing the size of the solution, that is, the size of the desired vertex set. In several applications, however, we also want to limit the “exposure” of the solution to the rest of… (More)

- Manuel Sorge, René van Bevern, Rolf Niedermeier, Mathias Weller
- J. Discrete Algorithms
- 2011

We provide a new characterization of the NP-hard arc routing problem Rural Postman in terms of a constrained variant of minimum-weight perfect matching on bipartite graphs. To this end, we employ a parameterized equivalence between Rural Postman and Eulerian Extension, a natural arc addition problem in directed multigraphs. We indicate the NP-hardness of… (More)

We present a linear-time kernelization algorithm that transforms a given planar graph G with domination number γ(G) into a planar graph G′ of size O(γ(G)) with γ(G) = γ(G′). In addition, a minimum dominating set for G can be inferred from a minimum dominating set for G′. In terms of parameterized algorithmics, this implies a linear-size problem kernel for… (More)