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International Conference on Current Trends in Theory and Practice of Informatics

SOFSEM 2016: SOFSEM 2016: Theory and Practice of Computer Science pp 161–170Cite as

On the Power of Laconic Advice in Communication Complexity

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9587))

Abstract

We continue the study of a recently introduced model of communication complexity with advice, focusing on the power of advice in the context of equality of bitstrings and divisibility of natural numbers. First, we establish that the equality problem admits a protocol of polylogarithmic communication, provided a laconic advice of just one bit. For the divisibility problem, we design a protocol with sublinear communication and advice of roughly \({\tilde{O}}(\sqrt{n})\). We complement our result on divisibility with a matching lower bound in a restricted setting using a recent result of Chattopadhyay et al. and a reduction from set-disjointness to divisibility.

This work was partially supported by SNF grant 200021-146372.

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References

  1. Hromkovič, J.: Communication Complexity and Parallel Computing. Springer, New York (1997)

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  2. Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, New York (1997)

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  3. Patrascu, M.: Towards polynomial lower bounds for dynamic problems. In: Schulman, L.J. (ed.) STOC, pp. 603–610. ACM (2010)

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  4. Chattopadhyay, A., Edmonds, J., Ellen, F., Pitassi, T.: A little advice can be very helpful. In: Rabani, Y. (ed.) SODA, pp. 615–625. SIAM (2012)

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Author information

Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Kfir Barhum & Juraj Hromkovič

Authors
  1. Kfir Barhum
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  2. Juraj Hromkovič
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Corresponding author

Correspondence to Kfir Barhum .

Editor information

Editors and Affiliations

  1. University of Latvia, Riga, Latvia

    Rūsiņš Mārtiņš Freivalds

  2. University of Paderborn, Paderborn, Germany

    Gregor Engels

  3. University of Genoa, Genoa, Italy

    Barbara Catania

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© 2016 Springer-Verlag Berlin Heidelberg

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Barhum, K., Hromkovič, J. (2016). On the Power of Laconic Advice in Communication Complexity. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_13

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  • DOI: https://doi.org/10.1007/978-3-662-49192-8_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49191-1

  • Online ISBN: 978-3-662-49192-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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