Coordinatized Kernels and Catalytic Reductions: An Improved FPT Algorithm for Max Leaf Spanning Tree and Other Problems

We describe some new, simple and apparently general methods for designing FPT algorithms, and illustrate how these can be used to obtain a significantly 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 payoffs 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.