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

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Noga Alon, Daniel Lokshtanov, Saket Saurabh
• Keywords: ICALP 2009, Space Parameterized Algorithm, Theoretical Computer Science, Time Parameterized Algorithm, Universal Coloring Families