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Automata, Languages and Programming (ICALP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5555))

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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.

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Author information

Authors and Affiliations

  1. Tel Aviv University, Tel Aviv, 69978, Israel

    Noga Alon

  2. IAS, Princeton, NJ, 08540, USA

    Noga Alon

  3. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Daniel Lokshtanov & Saket Saurabh

Authors
  1. Noga Alon
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  2. Daniel Lokshtanov
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  3. Saket Saurabh
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer and Systems Sciences, Sapienza University of Rome, Via Ariosto 25, 00184, Roma, Italy

    Alberto Marchetti-Spaccamela

  3. Google R&D Center, School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Yossi Matias

  4. University of Patras and CTI, N. Kazantzaki Street 1, 26504 Rion, Patras, Greece

    Sotiris Nikoletseas

  5. RWTH Aachen, Lehrstuhl Informatik 7, Ahornstraße 55, 52056, Aachen, Germany

    Wolfgang Thomas

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© 2009 Springer-Verlag Berlin Heidelberg

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Alon, N., Lokshtanov, D., Saurabh, S. (2009). Fast FAST . In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_6

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  • DOI: https://doi.org/10.1007/978-3-642-02927-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02926-4

  • Online ISBN: 978-3-642-02927-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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