We algorithmize the recent structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To complement these results, we establish that Dominating Set is not fixed-parameter tractable on the slightly larger class of graphs that excl...

We discuss the parameterised complexity of answering tree-shaped ontology-mediated queries (OMQs) in OWL 2 QL under various restrictions on their ontologies and conjunctive queries (CQs). In particular, we construct an ontology T such that answering OMQs (T , q) with tree-shaped CQs q is W[1]hard if the number of leaves in q is regarded as the parameter. The number of leaves has previously been...

This paper is concerned with the fixed-parameter tractability of the problem of deciding whether a graph can be made into a graph with a specified hereditary property by deleting at most i vertices, at most j edges, and adding at most k edges, where i, j, k are fixed integers. It is shown that this problem is fixed-parameter tractable whenever the hereditary property can be characterized by a f...

We study variants and generalizations of the problem of finding an r-regular subgraph (where r ≥ 3) in a given graph by deleting at most k vertices. Moser and Thilikos (2006) have shown that the problem is fixed-parameter tractable (FPT) if parameterized by (k, r). They asked whether the problem remains fixed-parameter tractable if parameterized by k alone. We answer this question negatively: w...

In this paper we study the parameterized complexity of the firefighter problem. More precisely, we show that Saving k-Vertices and its dual Saving All But k-Vertices are both W[1]-hard for parameter k even for bipartite graphs. We also investigate several cases for which the firefighter problem is tractable. For instance, Saving kVertices is fixed-parameter tractable on planar graphs for parame...

Let I be an instance of binary boolean CSP. Consider the problem of deciding whether one can remove at most k constraints of I such that the remaining constraints are satisfiable. We call it the Almost CSP problem. This problem is NP-complete and we study it from the point of view of parameterized complexity where k is the parameter. Two special cases have been studied: when the constraints are...

Computing posterior and marginal probabilities constitutes the backbone of almost all inferences in Bayesian networks. These computations are known to be intractable in general, both to compute exactly and to approximate by sampling algorithms. While it is well known under what constraints exact computation can be rendered tractable (viz., bounding tree-width of the moralized network and boundi...

The theory of n-fold integer programming has been recently emerging as an important tool in parameterized complexity. The input to an n-fold integer program (IP) consists of parameter A, dimension n, and numerical data of binary encoding length L. It was known for some time that such programs can be solved in polynomial time using O(ng(A)L) arithmetic operations where g is an exponential functi...

To decide if the parameterized feedback vertex set problem in directed graph is fixed-parameter tractable is a long time open problem. In this paper, we prove that the parameterized feedback vertex set in directed graph is fixed-parameter tractable and give the first FPT algorithm of running time O((1.48k)n) for it. As the feedback arc set problem in directed graph can be transformed to a feedb...