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On Multipartition Communication Complexity

(Extended Abstract)

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STACS 2001 (STACS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2010))

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Abstract

We study k-partition communication protocols, an extension of the standard two-party best-partition model to k input partitions. The main results are as follows.

  1. 1.

    A strong explicit hierarchy on the degree of non-obliviousness is established by proving that, using k+1 partitions instead of k may decrease the commu- nication complexity from θ (n) to θ (log k).

  2. 2.

    Certain linear codes are hard for k-partition protocols even when k may be exponentially large (in the input size). On the other hand, one can show that all characteristic functions of linear codes are easy for randomized OBDDs.

  3. 3.

    It is proven that there are subfunctions of the triangle-freeness function and the function ⊕ CLIQUEn,3 which are hard for multipartition protocols. As an application, truly exponential lower bounds on the size of nondeterministic read-once branching programs for these functions are obtained, solving an open problem of Razborov [17].

The work of the first and second author has been supported by DFG grant Hr 14/3-2, and of the fourth author by DFG grant We 1066/9-1.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik I RWTH Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Pavol Ďuriš & Juraj Hromkovič

  2. Department of Informatics, Comenius University Mlynska dolina, 84215, Bratislava, Slovakia

    Pavol Ďuriš

  3. Fachbereich Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Robert-Mayer-Straße 11-15, 60054, Frankfurt am Main, Germany

    Stasys Jukna & Georg Schnitger

  4. FB Informatik, LS 2, Universität Dortmund, 44221, Dortmund, Germany

    Martin Sauerhoff

Authors
  1. Pavol Ďuriš
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  2. Juraj Hromkovič
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  3. Stasys Jukna
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  4. Martin Sauerhoff
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  5. Georg Schnitger
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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Ďuriš, P., Hromkovič, J., Jukna, S., Sauerhoff, M., Schnitger, G. (2001). On Multipartition Communication Complexity. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_18

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  • DOI: https://doi.org/10.1007/3-540-44693-1_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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