Phylogenetic networks are used to display the relationship of different species whose evolution is not treelike, which is the case, for instance, in the presence of hybridization events or horizontal gene transfers. Tree inference methods such as Maximum Parsimony need to be modified in order to be applicable to networks. In this paper, we discuss two different definitions of Maximum Parsimony ...

We study the manipulation problem in elections with bounded singlepeaked width from the parameterized complexity point of view. In particular, we focus on the Borda, Copeland and Maximin voting correspondences. For Borda, we prove that the unweighted manipulation problem with two manipulators is fixed-parameter tractable with respect to single-peaked width. For Maximin and Copeland for every 0 ...

In the Directed k-Chinese Postman Problem (k-DCPP), we are given a connected weighted digraph G and asked to find k non-empty closed directed walks covering all arcs of G such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124–128) asked for the parameterized complexity of k-DCPP when k is the parameter. We prove that the k-DCPP is fixed-...

We study the parameterized complexity of the propositional model counting problem #SAT for CNF formulas. As the parameter we consider the treewidth of the following two graphs associated with CNF formulas: the consensus graph and the conflict graph. Both graphs have as vertices the clauses of the formula; in the consensus graph two clauses are adjacent if they do not contain a complementary pai...

Unless P = NP we have to satisfy ourselves with any two out of the three goals. Most of the early undergrad algorithms like matching, shortest path etc. are exact and fast. To tackle hard problems and obtain a fast solution we use approximation algorithms, PTAS etc. FPT or fixed parameter tractable algorithms come to our rescue when we need to tackle hard problems yet obtain an optimal solution...

We introduce a new approach for establishing fixed-parameter tractability of problems parameterized above tight lower bounds. To illustrate the approach we consider three problems of this type of unknown complexity that were introduced by Mahajan, Raman and Sikdar (J. Comput. Syst. Sci. 75, 2009). We show that a generalization of one of the problems and non-trivial special cases of the other tw...

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions Ss and St of size k, whether it is possible to transform Ss into St by a sequence of vertex additions and deletions such that each intermediate set is also a feasible solution of size bounded by k....

One of Courcelle’s celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width. In this paper we show that in terms of tree...

The NP-hard 2-Club problem is, given an undirected graph G = (V,E) and ` ∈ N, to decide whether there is a vertex set S ⊆ V of size at least ` such that the induced subgraph G[S] has diameter at most two. We make progress towards a systematic classification of the complexity of 2-Club with respect to a hierarchy of prominent structural graph parameters. First, we present the following tight NP-...