Fast FAST

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 F 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 f 2 F which is a proper vertex coloring of G. Our algorithm is the rst non-trivial subexponential time parameterized algorithm outside the framework of bidimensionality.