We give improved parameterized algorithms for two “edge” problems MAXCUT and MAXDAG, where the solution sought is a subset of edges. MAXCUT of a graph is a maximum set of edges forming a bipartite subgraph of the given graph. On the other hand, MAXDAG of a directed graph is a set of arcs of maximum size such that the graph induced on these arcs is acyclic. Our algorithms are obtained through ne...

Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider the class Wk(G), where for each graph G in Wk(G), the removal of a set of at most k vertices from...

We present a new and compelling approach to the efficient solution of important computational problems that arise in the context of abstract argumentation. Our approach makes known algorithms defined for restricted fragments generally applicable, at a computational cost that scales with the distance from the fragment. Thus, in a certain sense, we gradually augment tractable fragments. Surprisin...

Haplotyping via perfect phylogeny is a method for retrieving haplotypes from genotypes. Fast algorithms are known for computing perfect phylogenies from complete and error-free input instances—these instances can be organized as a genotype matrix whose rows are the genotypes and whose columns are the single nucleotide polymorphisms under consideration. Unfortunately, in the more realistic setti...

Article history: Received 29 February 2016 Received in revised form 27 June 2016 Accepted 25 July 2016 Available online 12 August 2016

The NP-hard Minimum Common String Partition problem asks whether two strings x and y can each be partitioned into at most k substrings such that both partitions use exactly the same substrings in a different order. We present the first fixed-parameter algorithm for Minimum Common String Partition using only parameter k.

Given a graph G cellularly embedded on a surface Σ of genus g, a cut graph is a subgraph of G such that cutting Σ along G yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any ε > 0, we show how to compute a (1 + ε) approximation of the shortest cut graph in time f(ε, g)n. Our techniques first...

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper we provide the first algorithmic applications of tree-cut width to hard combinatorial problems. Tree-cut width is known to be lower-bounded by a function of treewidth, but it can be much larger and hence has the poten...

Inclusion dependencies are one of the most important database constraints. In isolation their finite and unrestricted implication problems coincide, are finitely axiomatizable, PSPACE-complete, and fixed-parameter tractable in their arity. In contrast, finite and unrestricted implication problems for the combined class of functional and inclusion dependencies deviate from one another and are ea...

Lubiw showed that several variants of Graph Isomorphism are NPcomplete, where the solutions are required to satisfy certain additional constraints [14]. One of these, called Isomorphism With Restrictions, is to decide for two given graphs X1 = (V,E1) and X2 = (V,E2) and a subset R ⊆ V × V of forbidden pairs whether there is an isomorphism π from X1 to X2 such that i π 6= j for all (i, j) ∈ R. W...