 
Summary: Fast FAST
Noga Alon1
Daniel Lokshtanov2
Saket Saurabh2
1
Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ, 08540, USA.
nogaa@tau.ac.il
2
Department of Informatics, University of Bergen, N5020 Bergen, Norway.
{daniellosaket.saurabh}@ii.uib.no
Abstract. We present a randomized subexponential time, polynomial space parameterized
algorithm for the kWeighted Feedback Arc Set in Tournaments (kFAST) 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 nontrivial subexponential time parameterized algorithm outside the framework of
bidimensionality.
1 Introduction
