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...

Given a set P of points in the Euclidean plane and two triangulations P, flip distance between these is minimum number flips required to transform one triangulation into other. The Parameterized Flip Distance problem decide if given equal integer k. previous best FPT algorithm runs time O?(k?ck) (c?2×1411), where each step has fourteen possible choices, length action sequence bounded by 11k. By...

This paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants. The first problem is the Rectilinear Line Cover where the inputs are n points in R and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines where these lines are restricted to be axis parallel. We show that this problem has efficie...