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Randomized distributed decision

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Abstract

The paper tackles the power of randomization in the context of local distributed computing by analyzing the ability to “boost” the success probability of deciding a distributed language using a Monte-Carlo algorithm. We prove that, in many cases, the ability to increase the success probability for deciding distributed languages is rather limited. This contrasts with the sequential computing setting where boosting can systematically be achieved by repeating the randomized execution.

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Notes

  1. LCL is essentially \(\mathrm{LD}(O(1))\) restricted to languages involving graphs of constant maximum degree and processor inputs taken from a set of constant size.

  2. There is a fundamental difference between such tasks when locality is concerned. Indeed, whereas the validity of constructing a problem in LCL is local (by definition), the validity in our setting is “global”, in the sense that in an illegal instance, it is sufficient that at least one vertex in the entire network outputs “no”.

  3. Note that an undecidable collection of instances remains undecidable in the distributed setting too.

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Authors and Affiliations

  1. CNRS, University Paris Diderot, Paris, France

    Pierre Fraigniaud & Amos Korman

  2. Department of Computer Science, University of Toronto, Toronto, Canada

    Mika Göös

  3. The Weizmann Institute of Science, Rehovot, Israel

    Merav Parter & David Peleg

Authors
  1. Pierre Fraigniaud
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  2. Mika Göös
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  3. Amos Korman
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  4. Merav Parter
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  5. David Peleg
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Corresponding author

Correspondence to Amos Korman.

Additional information

A. Korman: Supported by the ANR project DISPLEXITY, and by the INRIA project GANG.

M. Parter: Additional support from the Google European Fellowship in distributed computing.

D. Peleg: Supported in part by the Israel Science Foundation (grant 894/09), the United States-Israel Binational Science Foundation (grant 2008348), the I-CORE program of the Israel PBC and ISF (grant 4/11), the Israel Ministry of Science and Technology (infrastructures grant), and the Citi Foundation.

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Fraigniaud, P., Göös, M., Korman, A. et al. Randomized distributed decision. Distrib. Comput. 27, 419–434 (2014). https://doi.org/10.1007/s00446-014-0211-x

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  • DOI: https://doi.org/10.1007/s00446-014-0211-x

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