Fast FAST

Abstract

We present a randomized subexponential time, polynomial space parameterized algorithm for the k -Weighted Feedback Arc Set in Tournaments (k -FAST) problem. We also show that our algorithm can be derandomized by slightly increasing the running time. To derandomize our algorithm we construct a new kind of universal hash functions, that we coin universal coloring families. For integers m,k and r, a family of functions from [m] to [r] is called a universal (m,k,r)-coloring family if for any graph G on the set of vertices [m] with at most k edges, there exists an which is a proper vertex coloring of G. Our algorithm is the first non-trivial subexponential time parameterized algorithm outside the framework of bidimensionality. © 2009 Springer Berlin Heidelberg.