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...

A Fixed-Parameter Tractable (FPT) ρ-approximation algorithm for a minimization (resp. maximization) parameterized problem P is an FPT-algorithm that, given an instance (x, k) ∈ P computes a solution of cost at most k · ρ(k) (resp. k/ρ(k)) if a solution of cost at most (resp. at least) k exists; otherwise the output can be arbitrary. For well-known intractable problems such as the W[1]-hard Cliq...

There is a computable function f such that the problem of deciding, given a word w and an MSO sentence φ whether, S w |= φ can be decided in time O(f (l)n) where l is the length of φ and n is the length of w.

As a generalization of paths, the notion of paths of bandwidth w is introduced. We show that, for constant w ≥ 1, the corresponding search problem for such a path of length k in a given graph is NP-complete and fixed-parameter tractable (FPT) in the parameter k, like this is known for the special case w = 1, the LONGEST PATH problem. We state the FPT algorithm in terms of a guess and check prot...

We show that for any fixed i, j ≥ 1, the k-Dominating Set problem restricted to graphs that do not have Ki,j as a subgraph is fixed parameter tractable (FPT) and has a polynomial kernel. This result implies that this problem restricted to bounded-degenerate graphs has a polynomial kernel, solving an open problem posed by Alon and Gutner in [3]. Our result extends the class of graphs for which t...

Given a set of obstacles and two points in the plane, is there a path between the two points that does not cross more than k different obstacles? Equivalently, can we remove k obstacles so that there is an obstacle-free path between the two designated points? This is a fundamental problem that has undergone a tremendous amount of work by researchers in various areas, including computational geo...