Abstract. We describe some new, simple and apparently general methods for designing FPT algorithms, and illustrate how these can be used to obtain a signi cantly improved FPT algorithm for the Maximum Leaf Spanning Tree problem. Furthermore, we sketch how the methods can be applied to a number of other well-known problems, including the parametric dual of Dominating Set (also known as Nonblocker), Matrix Domination, Edge Dominating Set, and Feedback Vertex Set for Undirected Graphs. The main payo s of these new methods are in improved functions f(k) in the FPT running times, and in general systematic approaches that seem to apply to a wide variety of problems.
Michael R. Fellows, Catherine McCartin, Frances A.