Path-width of matroids naturally generalizes better known path-width of graphs, and is NP-hard by a reduction from the graph case. While the term matroid path-width was formally introduced by Geelen–Gerards–Whittle [JCTB 2006] in pure matroid theory, it was soon recognized by Kashyap [SIDMA 2008] that it is the same concept as long-studied so called trellis complexity in coding theory, later na...

Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one way of obtaining strongly uniform FPT algorithms, but that all of FPT may be captured in this way. Our new characterization of FPT has a strong connection to...

Following colostrum management training, a randomized field trial was conducted on a California dairy to determine the effect of supplementing pooled colostrum with either colostrum-derived replacer (CDR) or second-milking colostrum (transition milk) on failure of passive transfer (FPT) and preweaning morbidity risks. A total of 166 calves were randomly assigned to 4L first-milking pooled colos...

We study the parameterized complexity of several NP-Hard graph completion problems: The MINIMUM FILL-IN problem is to decide if a graph can be triangulated by adding at most k edges. We develop an O(k 5 mn + f(k)) algorithm for the problem on a graph with n vertices and m edges. In particular, this implies that the problem is xed parameter tractable (FPT). PROPER INTERVAL GRAPH COMPLETION probl...

We study the complexity of a group of distance-constrained graph labeling problems when parameterized by the neighborhood diversity (nd), which is a natural graph parameter between vertex cover and clique width. Neighborhood diversity has been used to generalize and speed up FPT algorithms previously parameterized by vertex cover, as is also demonstrated by our paper. We show that the Uniform C...

Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set X n points and two numbers k m, clustering aims to exclude m from X, partition remaining into clusters that minimizes certain cost function. In this paper, we give general approach for solving outliers, which results fixed-parameter tractable (FPT) algorithm (i.e., an running time form f(k, m) * po...

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...