Fast FAST

  • Authors:

  • Noga Alon;Daniel Lokshtanov;Saket Saurabh

  • Affiliations:

  • Tel Aviv University, Tel Aviv, Israel 69978 and IAS, Princeton, USA 08540;Department of Informatics, University of Bergen, Bergen, Norway N-5020;Department of Informatics, University of Bergen, Bergen, Norway N-5020

  • Venue:
  • ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
  • Year:
  • 2009

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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 ${\mathcal F}$ 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 $f \in {\mathcal F}$ which is a proper vertex coloring of G . Our algorithm is the first non-trivial subexponential time parameterized algorithm outside the framework of bidimensionality.