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Brief Announcement: Deterministic Graph Connectivity in the Broadcast Congested Clique

Published: 25 July 2016 Publication History

Abstract

We present deterministic constant-round protocols for the graph connectivity problem in the model where each of the n nodes of a graph receives a row of the adjacency matrix, and broadcasts a single sublinear size message to all other nodes. Communication rounds are synchronous. This model is sometimes called the broadcast congested clique. Specifically, we exhibit a deterministic protocol that computes the connected components of the input graph in [1/ε] rounds, each player communicating O(nε ⋅ log n) bits per round, with 0 < ε ≤ 1.
We also provide a deterministic one-round protocol for connectivity, in the model when each node receives as input the graph induced by the nodes at distance at most r>0, and communicates O(n1/r ⋅ log n) bits. This result is based on a d-pruning protocol, which consists in successively removing nodes of degree at most $d$ until obtaining a graph with minimum degree larger than d. Our technical novelty is the introduction of deterministic sparse linear sketches: a linear compression function that permits to recover sparse Boolean vectors deterministically.

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K. J. Ahn, S. Guha, and A. McGregor. Graph sketches: Sparsification, spanners, and subgraphs. In Proc. of the 31st Symposium on Principles of Database Systems, PODS '12, pages 5--14, 2012.
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B. Awerbuch, O. Goldreich, R. Vainish, and D. Peleg. A trade-off between information and communication in broadcast protocols. J. ACM, 37(2):238--256, Apr. 1990.
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J. W. Hegeman, G. Pandurangan, S. V. Pemmaraju, V. B. Sardeshmukh, and M. Scquizzato. Toward optimal bounds in the congested clique: Graph connectivity and mst. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC '15, pages 91--100, New York, USA, 2015. ACM.
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Cited By

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  • (2024)Universally Optimal Information Dissemination and Shortest Paths in the HYBRID Distributed ModelProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662791(380-390)Online publication date: 17-Jun-2024
  • (2021)Tight distributed sketching lower bound for connectivityProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458175(1856-1873)Online publication date: 10-Jan-2021
  • (2020)Graph reconstruction in the congested cliqueJournal of Computer and System Sciences10.1016/j.jcss.2020.04.004Online publication date: May-2020
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cover image ACM Conferences
PODC '16: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
July 2016
508 pages
ISBN:9781450339643
DOI:10.1145/2933057
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Publication History

Published: 25 July 2016

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Author Tags

  1. broadcast congested clique
  2. deterministic protocol
  3. graph connectivity
  4. spanning forest

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PODC '16 Paper Acceptance Rate 40 of 149 submissions, 27%;
Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

View all
  • (2024)Universally Optimal Information Dissemination and Shortest Paths in the HYBRID Distributed ModelProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662791(380-390)Online publication date: 17-Jun-2024
  • (2021)Tight distributed sketching lower bound for connectivityProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458175(1856-1873)Online publication date: 10-Jan-2021
  • (2020)Graph reconstruction in the congested cliqueJournal of Computer and System Sciences10.1016/j.jcss.2020.04.004Online publication date: May-2020
  • (2020)The role of randomness in the broadcast congested clique modelInformation and Computation10.1016/j.ic.2020.104669(104669)Online publication date: Nov-2020
  • (2019)Connectivity Lower Bounds in Broadcast Congested CliqueProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331569(256-258)Online publication date: 16-Jul-2019
  • (2018)MST in O(1) rounds of congested cliqueProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3174304.3175472(2620-2632)Online publication date: 7-Jan-2018
  • (2018)The Impact of Locality on the Detection of Cycles in the Broadcast Congested Clique ModelLATIN 2018: Theoretical Informatics10.1007/978-3-319-77404-6_11(134-145)Online publication date: 13-Mar-2018
  • (2018)Connectivity and Minimum Cut Approximation in the Broadcast Congested CliqueStructural Information and Communication Complexity10.1007/978-3-030-01325-7_28(331-344)Online publication date: 31-Oct-2018
  • (2018)Communication Complexity in Vertex Partition Whiteboard ModelStructural Information and Communication Complexity10.1007/978-3-030-01325-7_24(264-279)Online publication date: 31-Oct-2018
  • (2018)Two Rounds Are Enough for Reconstructing Any Graph (Class) in the Congested Clique ModelStructural Information and Communication Complexity10.1007/978-3-030-01325-7_15(134-148)Online publication date: 31-Oct-2018
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