Summary: Fast FAST
Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ, 08540, USA.
Department of Informatics, University of Bergen, N-5020 Bergen, Norway.
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 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 F which is a proper vertex coloring of G. Our algorithm
is the first non-trivial subexponential time parameterized algorithm outside the framework of