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Communication Lower Bounds Via the Chromatic Number

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FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4855))

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Abstract

We present a new method for obtaining lower bounds on communication complexity. Our method is based on associating with a binary function f a graph G f such that logχ(G f ) captures N 0(f) + N 1(f). Here χ(G) denotes the chromatic number of G, and N 0(f) and N 1(f) denote, respectively, the nondeterministic communication complexity of \(\overline{f}\) and f. Thus logχ(G f ) is a lower bound on the deterministic as well as zero-error randomized communication complexity of f. Our characterization opens the possibility of using various relaxations of the chromatic number as lower bound techniques for communication complexity. In particular, we show how various (known) lower bounds can be derived by employing the clique number, the Lovász ϑ-function, and graph entropy lower bounds on the chromatic number.

This work was performed while the authors were at IBM Almaden.

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Authors and Affiliations

  1. Yahoo! Research, USA

    Ravi Kumar

  2. Google, Inc., USA

    D. Sivakumar

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  1. Ravi Kumar
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  2. D. Sivakumar
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V. Arvind Sanjiva Prasad

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Kumar, R., Sivakumar, D. (2007). Communication Lower Bounds Via the Chromatic Number. In: Arvind, V., Prasad, S. (eds) FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2007. Lecture Notes in Computer Science, vol 4855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77050-3_19

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  • DOI: https://doi.org/10.1007/978-3-540-77050-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77049-7

  • Online ISBN: 978-3-540-77050-3

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