We show that the DOMINATING SET problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K1,3, the complete bipartite graph on four vertices where the two parts have one and three vertices, respectively) as an induced subgraph. We present an algorithm that uses 2 2)nO(1) time and polynomial space to decide whether a claw-free graph on n v...

PURPOSE The authors assessed comorbidity of auditory processing disorder (APD), language impairment (LI), and reading disorder (RD) in school-age children. METHOD Children (N = 68) with suspected APD and nonverbal IQ standard scores of 80 or more were assessed using auditory, language, reading, attention, and memory measures. Auditory processing tests included the Frequency Pattern Test (FPT;...

An (r, t)-FPT-hardness in opt is finding some instance I whose optimum value opt is known and proving that the problem admits no r(opt) approximation that runs in time t(opt)|I|O(1). The usual definition uses r(k)-inapproximability in time t(k) · |I|O(1), for some k ≥ opt in minimization problems, and opt ≤ k for maximization problems. If opt is known then inapproximability in opt implies inapp...

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the treewidth minors. In this paper, we provide first algorithmic applications of hard combinatorial problems. Tree-cut is known be lower-bounded by function treewidth, but it can much larger and hence has potential facilitate efficient solution problems that are not fixed-parameter tractab...

Graph modification problems such as vertex deletion, edge deletion or edge contractions are a fundamental class of optimization problems. Recently, the parameterized complexity of the contractibility problem has been pursued for various specific classes of graphs. Usually, several graph modification questions of the deletion variety can be seen to be FPT if the graph class we want to delete int...

A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of the integers assigned to its ends. For many application one hopes to find an LA with small cost. However, it is a classical NP-complete problem to decide wh...

Given a list of k source-sink pairs in an edge-weighted graph G, the minimum multicut problem consists in selecting a set of edges of minimum total weight in G, such that removing these edges leaves no path from each source to its corresponding sink. To the best of our knowledge, no non-trivial FPT result for special cases of this problem, which is APX-hard in general graphs for any fixed k ≥ 3...

This article reviews recent empirical and brain imaging data on effects of cognitive training methods on complex interactive skill learning, and presents a neurally inspired computational model that characterizes the effects of these training methods. In particular, the article focuses on research that shows that variable priority training (VPT), which requires learners to shift their prioritie...

The parameterized complexity classes of the W -hierarchy are usually defined as the problems reducible to certain natural complete problems by means of fixed-parameter tractable (fpt) reductions. We investigate whether the classes can be characterised by means of weaker, logical reductions. We show that each class W [t] has complete problems under slicewise bounded-variable firstorder reduction...

In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n) time for some function f(k) and constant d. Though FPT algorithms have been successfully designed for many problems, typically they are not sufficiently fast because of huge f(k) and d. In this p...