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Communication in the presence of replication

Published: 17 May 2008 Publication History

Abstract

We consider the following problem. Suppose that a big amount of data is distributed among several parties, so that each party misses only few pieces of data. The parties wish to perform some global computation on the data while minimizing the communication between them. This situation is common in many real-life scenarios. A naive solution to this problem is to first perform a synchronization step, letting one party learn all pieces of data, and then let this party perform the required computation locally. We study the question of obtaining better solutions to the problem, focusing mainly on the case of computing low-degree polynomials via non-interactive protocols. We present interesting connections between this problem and the well studied cryptographic problem of secret sharing. We use this connection to obtain nontrivial upper bounds and lower bounds using results and techniques from the domain of secret sharing. The relation with open problems from the area of secret sharing also provides evidence for the difficulty of resolving some of the questions we leave open.

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  • (2009)On the complexity of communication complexityProceedings of the forty-first annual ACM symposium on Theory of computing10.1145/1536414.1536479(465-474)Online publication date: 31-May-2009

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    cover image ACM Conferences
    STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing
    May 2008
    712 pages
    ISBN:9781605580470
    DOI:10.1145/1374376
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    Published: 17 May 2008

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    Author Tags

    1. communication complexity
    2. secret sharing
    3. simultaneous messages

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    May 17 - 20, 2008
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    • (2009)On the complexity of communication complexityProceedings of the forty-first annual ACM symposium on Theory of computing10.1145/1536414.1536479(465-474)Online publication date: 31-May-2009

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