This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area.Expand

We show that all problems expressible in Counting Monadic Second Order Logic and satisfying a compactness condition admit a polynomial kernel on graphs of bounded genus.Expand

We present a randomized subexponential time, polynomial space parameterized algorithm for the k -Weighted Feedback Arc Set in Tournaments (k -FAST ) problem.Expand

In parameterized complexity each problem instance comes with a parameter k , and a parameterized problem is said to admit a kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size k .Expand

A central problem in parameterized algorithms is to obtain algorithms with running time <i>f</i>(<i>k</i>) such that the dependence on the parameter is as slow growing function of the parameter as possible.Expand

We give two algorithms computing representative families of linear and uniform matroids and demonstrate how to use representative families for designing single-exponential parameterized and exact exponential time algorithms.Expand