University Leipzig, Department of Computer Science and Interdisciplinary Center for Bioinformatics, 04107 Leipzig, Germany; University of Vienna, Faculty of Chemistry, Department of Theoretical Chemistry, 1090 Vienna, Austria; University of Vienna, Faculty of Computer Science, Research Group Bioinformatics and Computational Biology, 1090 Vienna, Austria; CNRS UMR 7161 LIX, Ecole Polytechnique, ...

We investigate the parameterized complexity of Maximum Independent Set and Dominating Set restricted to certain geometric graphs. We show that Dominating Set is W[1]-hard for the intersection graphs of unit squares, unit disks, and line segments. For Maximum Independent Set, we show that the problem is W[1]-complete for unit segments, but fixed-parameter tractable if the segments are axis-paral...

A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph on n vertices contains a feedback vertex set (FVS) of size at most k, in time 2k!O(n). This is the first fixed parameter tractable algorithm for FVS that applies to both directed and undirected graphs.

String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NP-hard. This motivates the search for (fixed-parameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NP-hard string problems and identify challenges for future research.

We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem. In particular, we provide fixed parameter tractable algorithms for the 1-page book crossing number, the 2-page book crossing number, and the minimum number of crossed edges in 1-page and 2-page book drawings.

A graph is H-free if it has no induced subgraph isomorphic to H. We determine the computational complexity of the Choosability problem restricted to H-free graphs for every graph H that does not belong to {K1,3, P1 +P2, P1 +P3, P4}. We also show that if H is a linear forest, then the problem is fixed-parameter tractable when parameterized by k.

We present a list of parameterized problems together with a complexity classification of whether they allow a fixed-parameter tractable reduction to SAT or not. These parameterized problems are based on problems whose complexity lies at the second level of the Polynomial Hierarchy or higher. The list will be updated as necessary.

The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournaments, a well studied class of directed graphs. We consider both weighted and unweighted versions. W...

The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the Tractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computational-level theories of cognition. To utilize this constraint, a preci...

The Gene-Duplication Problem is the problem of computing the optimal species tree for a given set of gene trees under the Gene-Duplication Model ((rst introduced by Goodman et al.). The problem is known to be NP-complete. We give a xed-parameter tractable algorithm solving the problem parameterized by the number of gene duplications necessary to rectify the gene trees with the species tree.