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Fast Distributed Algorithms for Testing Graph Properties

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Distributed Computing (DISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9888))

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Abstract

We provide a thorough study of distributed property testing – producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called dense graph testing model we emulate sequential tests for nearly all graph properties having 1-sided tests, while in the general and sparse models we obtain faster tests for triangle-freeness, cycle-freeness and bipartiteness, respectively. In addition, we show a logarithmic lower bound for testing bipartiteness and cycle-freeness, which holds even in the LOCAL model.

In most cases, aided by parallelism, the distributed algorithms have a much shorter running time as compared to their counterparts from the sequential querying model of traditional property testing. The simplest property testing algorithms allow a relatively smooth transitioning to the distributed model. For the more complex tasks we develop new machinery that may be of independent interest.

Supported in part by the Israel Science Foundation (grant 1696/14).

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Notes

  1. 1.

    This was recently independently and concurrently devised in [16] for a different use.

  2. 2.

    Pipelining means that each vertex has a buffer for each edge, which holds the information (edges between chosen vertices, in our case) it needs to send over that edge. The vertex sends the pieces of information one after the other.

  3. 3.

    A graph G is said to be perfect if for every induced subgraph \(G'\) of G, the chromatic number of \(G'\) equals the size of the largest clique in \(G'\).

  4. 4.

    A more involved analysis of multiple prioritized BFS executions was used in [24], allowing all BFS executions to fully finish in a short time without too much delay due to congestion. Since we require a much weaker guarantee, we can avoid the strong full-fledged prioritization algorithm of [24] and settle for a simple rule that keeps one BFS tree alive. Also, the multiple BFS construction of [27] does not fit our demands as it may not reach all desired vertices within the required distance, in case there are many vertices that are closer.

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Authors and Affiliations

  1. Department of Computer Science, Technion – Israel Institute of Technology, Haifa, Israel

    Keren Censor-Hillel, Eldar Fischer, Gregory Schwartzman & Yadu Vasudev

Authors
  1. Keren Censor-Hillel
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  2. Eldar Fischer
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  3. Gregory Schwartzman
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  4. Yadu Vasudev
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Corresponding author

Correspondence to Gregory Schwartzman .

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Editors and Affiliations

  1. LABRI, Univ of Bordeaux LABRI, Talence Cedex, France

    Cyril Gavoille

  2. CNRS, Universite Bordeaux 1 CNRS, Talence Cedex, France

    David Ilcinkas

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Censor-Hillel, K., Fischer, E., Schwartzman, G., Vasudev, Y. (2016). Fast Distributed Algorithms for Testing Graph Properties. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_4

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  • DOI: https://doi.org/10.1007/978-3-662-53426-7_4

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