In this paper we give a programmatic overview of parame-terized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how xed-parameter tractability techniques can deliver practical algorithms in two diierent ways: (1) by providing useful exact algorithms for small parameter ranges, and (2) by providing guidance in the...

Stereotypy (e.g., repetitive hand waving) is a key phenotype of autism spectrum disorder, Fragile X and Rett syndromes, and other neuropsychiatric disorders, and its severity correlates with cognitive and attention deficits. There are no effective treatments, however, for stereotypy. Perturbation of serotonin (5-HT) neurotransmission contributes to stereotypy, suggesting that distinct 5-HT rece...

A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by branch and bound. This technique is general and the resulting time complexity has a low dependency on the parameter. However, the time complexity often becomes...

Given a digraph D, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in D an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time solvable for acyclic digraphs. In general, MinLOB is NPhard and we consider three parameterizations of MinLOB. We prove that two of them are NP-complete for every val...

An out-branching and an in-branching of a digraph D are called kdistinct if each of them has k arcs absent in the other. Bang-Jensen, Saurabh and Simonsen (2016) proved that the problem of deciding whether a strongly connected digraph D has k-distinct out-branching and inbranching is fixed-parameter tractable (FPT) when parameterized by k. They asked whether the problem remains FPT when extende...

We describe an algorithm for the FEEDBACK VERTEX SET problem on undirected graphs, parameterized by the size k of the feedback vertex set, that runs in time O(ckn3) where c = 10.567 and n is the number of vertices in the graph. This improves on the best previous FPT algorithms due to [RSS02, KPS04] and [RS05] that have running times of the form O ∗(2O(k lg lg ) and O∗(2O(k lg k lg lg k ), respe...

It often happens that although a problem is FPT, the practitioners prefer to use imprecise heuristic methods to solve the problem in the real-world situation simply because of the fact that the heuristic methods are faster. In this paper we argue that in this situation an FPT algorithm for the given problem may be still of a considerable practical use. In particular, the FPT algorithm can be us...

BACKGROUND Robot assisted gait training (RAGT) is considered to be a promising approach for improving gait-related gross motor function of children and youth with cerebral palsy. However, RAGT has yet to be empirically demonstrated to be effective. This knowledge gap is particularly salient given the strong interest in this intensive therapy, the high cost of the technology, and the requirement...

We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N , and an integer K. The goal is to find up to K sets from S that jointly cover (i.e., include) as many elements as possible. This problem is well-known to be NP-hard and, under stan...

The SRY-related gene SOX9 is involved in the differentiation of Sertoli cells in male gonads of vertebrates with different kinds of sex determination. In the olive ridley Lepidochelys olivacea, a species with temperature sex determination (TSD), the SOX9 protein is expressed at stages 21-24 in medullary cells in gonads of embryos incubated at both male-(MPT) or female-promoting temperatures (FP...