René van Bevern

Measuring indifference: unit interval vertex deletion

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 in difference between data items. We present a fixed-parameter algorithm based on the iterative compression technique that finds in O((14k+14)k+1kn6) time a set of k vertices whose deletion from an n-vertex graph makes it unit interval. Additionally, we show that making a graph chordal by at most k vertex deletions is NP-complete even on {claw, net, tent}-free graphs.

Linear-Time computation of a linear problem kernel for dominating set on planar graphs

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 the NP-hard Dominating Set problem on planar graphs, where the kernelization takes linear time. This improves on previous kernelization algorithms that provide linear-size kernels in cubic time.

Myhill-Nerode Methods for Hypergraphs

We introduce a method of applying Myhill-Nerode methods from formal language theory to hypergraphs and show how this method can be used to obtain the following parameterized complexity results.

A Parameterized Complexity Analysis of Combinatorial Feature Selection Problems

We examine the algorithmic tractability of NP-hard combinatorial feature selection problems in terms of parameterized complexity theory. In combinatorial feature selection, one seeks to discard dimensions from high-dimensional data such that the resulting instances fulfill a desired property. In parameterized complexity analysis, one seeks to identify relevant problem-specific quantities and tries to determine their influence on the computational complexity of the considered problem. In this paper, for various combinatorial feature selection problems, we identify parameterizations and reveal to what extent these govern computational complexity. We provide tractability as well as intractability results; for example, we show that the Distinct Vectors problem on binary points is polynomial-time solvable if each pair of points differs in at most three dimensions, whereas it is NP-hard otherwise.

Precedence-Constrained Scheduling Problems Parameterized by Partial Order Width

Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1-2):533-562), we show that P2|prec,

H-index manipulation by merging articles: models, theory, and experiments

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Parameterized Complexity of DAG Partitioning

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Towards Optimal and Expressive Kernelization for d -Hitting Set

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Kernelization through tidying: a case study based on s -plex cluster vertex deletion

, the problem of finding a non-preemptive minimum-makespan schedule for precedence-constrained jobs of lengths 1 and 2 on two parallel identical machines, is W[2]-hard parameterized by the width of the partial order giving the precedence constraints. To this end, we show that Shuffle Product, the problem of deciding whether a given word can be obtained by interleaving the letters of

On the Parameterized Complexity of Computing Balanced Partitions in Graphs

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