Consider a graph G = (V, E) and a coloring c of vertices with colors from [l]. A vertex v is said to be happy with respect to c if c(v) = c(u) for all neighbors u of v. Further, an edge (u, v) is happy if c(u) = c(v). Given a partial coloring c of V, the Maximum Happy Vertex (Edge) problem asks for a total coloring of V extending c to all vertices of V that maximises the number of happy vertice...

A challenging task in computational biology is the reconstruction of genomic sequences of extinct ancestors, given the phylogenetic tree and the sequences at the leafs. This task is best solved by calculating the most likely estimate of the ancestral sequences, along with the most likely edge lengths. We deal with this problem and also the variant in which the phylogenetic tree in addition to t...

This survey reviews the basic notions of parameterized complexity, and describes some new approaches to designing FPT algorithms and problem reductions for graph problems.

One of the biggest experimental programs helping to improve nuclear installation safety is PHEBUS, an international cooperative research program that provides data for validating computer codes dedicated analysis severe accidents and their calculation results. In European Union, HORIZON 2020 EURATOM project MUSA (Management Uncertainties Severe Accidents) in progress. Modelling PHEBUS FPT-1 tes...

Fixed-parameter tractability (FPT) techniques have recently been successful in solving NP-complete problem instances of practical importance which were too large to be solved with previous methods. In this paper, we show how to enhance this approach through the addition of parallelism, thereby allowing even larger problem instances to be solved in practice. More precisely, we demonstrate the po...

BACKGROUND Anorexia nervosa (AN) is a serious illness leading to substantial morbidity and mortality. The treatment of AN very often is protracted; repeated hospitalizations and lost productivity generate substantial economic costs in the health care system. Therefore, this study aimed to determine the differential cost-effectiveness of out-patient focal psychodynamic psychotherapy (FPT), enhan...

Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|), where f is an arbitrary function of some parameter p of the input x and poly is some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width, rankwidth, and booleanwidth are parameters often used in the design and analysis of such algorithms for problems on graphs. We show asymptotically almost surely (aas), b...

Poljak and Turzík (Discrete Mathematics 1986) introduced the notion of λ-extendible properties of graphs as a generalization of the property of being bipartite. They showed that for any 0 < λ < 1 and λ-extendible property Π, any connected graph G on n vertices and m edges contains a spanning subgraph H ∈ Π with at least λm+ 1−λ 2 (n−1) edges. The property of being bipartite is λ-extendible for ...

We study the parametrized complexity of the knot (and link) polynomials known as Jones polynomials, Kauuman polynomials and Hommy-polynomials. It is known that computing these polynomials is ]P hard in general. We look for parameters of the combinatorial presentation of knots and links which make the computation of these polynomials to be xed parameter tractable, i.e. to be in FPT. If the link ...

BACKGROUND The follow-up rate, a standard index of the completeness of follow-up, is important for assessing the validity of a cohort study. A common method for estimating the follow-up rate, the "Percentage Method", defined as the fraction of all enrollees who developed the event of interest or had complete follow-up, can severely underestimate the degree of follow-up. Alternatively, the media...