Recognition of minimal unsatisfiable CNF formulas (unsatisfiable CNF formulas which become satisfiable if any clause is removed) is a classical DP -complete problem. It was shown recently that minimal unsatisfiable formulas with n variables and n + k clauses can be recognized in time nO(k). We improve this result and present an algorithm with time complexity O(2kn4); hence the problem turns out...

In the framework of parameterized complexity, one of the most commonly used structural parameters is the treewidth of the input graph. The reason for this is that most natural graph problems turn out to be fixed parameter tractable when parameterized by treewidth. However, Graph Layout problems are a notable exception. In particular, no fixed parameter tractable algorithms are known for the Cut...

We systematically investigate the complexity of model checking the existential positive fragment of firstorder logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted to fall into the set; a natural question is then to classify which sentence sets are tractable and which are intractable. With respect to fixed-parameter tract...

The deficiency of a propositional formula F in CNF with n variables and m clauses is defined as m−n. It is known that minimal unsatisfiable formulas (unsatisfiable formulas which become satisfiable by removing any clause) have positive deficiency. Recognition of minimal unsatisfiable formulas is NP-hard, and it was shown recently that minimal unsatisfiable formulas with deficiency k can be reco...

The notions of cutwidth and pathwidth of digraphs play a central role in the containment theory for tournaments, or more generally semi-complete digraphs, developed in a recent series of papers by Chudnovsky, Fradkin, Kim, Scott, and Seymour [2, 3, 4, 8, 9, 11]. In this work we introduce a new approach to computing these width measures on semi-complete digraphs, via degree orderings. Using the ...

We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We show that for every k, the satisfiability above average of ordering CSPs of arity at most k is fixed-parameter tractable.

We show that neither Resolution nor tree-like Resolution is automatizable unless the class W[P] from the hierarchy of parameterized problems is fixed-parameter tractable by randomized algorithms with one-sided error.

Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NPcomplete, but its complexity depends on a parameter, usually a set of relations, upon which they are constructed. Following the parameter, there exist tractable and intractable instances of CSPs. In this paper we show a dichotomy theorem for every finite do...

We prove that for any integer generalized scoring rules (GSRs), winner determination and computing a wide range of strategic behavior are fixed-parameter tractable (FPT) w.r.t. the number of alternatives.

The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest” to the given set of permutations. Unfortunately, the problem is NP-hard. We provide a broad study of the parameterized complexity for computing optimal Kemeny rankings. Be...