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Brief Announcement: What Can We Compute in a Single Round of the Congested Clique?

Published: 16 June 2023 Publication History

Abstract

We show that any one-round algorithm that computes a minimum spanning tree (MST) in the unicast congested clique must use a link bandwidth of Ω(log3 n) bits in the worst case. Consequently, computing an MST under the standard assumption of O(log n)-size messages requires at least 2 rounds. This is the first round complexity lower bound in the unicast congested clique for a problem where the output size is small, i.e., O(n log n) bits. Our lower bound holds as long as every edge of the MST is output by an incident node. To the best of our knowledge, all prior lower bounds for the unicast congested clique either considered problems with large output sizes (e.g., subgraph enumeration) or required every node to learn the entire output.

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Cited By

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  • (2025)The Voronoi Diagram of Weakly Smooth Planar Point Sets in $$O(\log n)$$ Deterministic Rounds on the Congested CliqueComputing and Combinatorics10.1007/978-981-96-1093-8_39(478-489)Online publication date: 20-Feb-2025
  • (2024)Boolean Matrix Multiplication for Highly Clustered Data on the Congested CliqueEuro-Par 2024: Parallel Processing10.1007/978-3-031-69583-4_4(45-58)Online publication date: 26-Aug-2024

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  1. Brief Announcement: What Can We Compute in a Single Round of the Congested Clique?

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    cover image ACM Conferences
    PODC '23: Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing
    June 2023
    392 pages
    ISBN:9798400701214
    DOI:10.1145/3583668
    Permission to make digital or hard copies of all or part 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 components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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    Published: 16 June 2023

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    Author Tags

    1. congested clique
    2. distributed graph algorithm
    3. lower bound

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    PODC '23 Paper Acceptance Rate 29 of 110 submissions, 26%;
    Overall Acceptance Rate 740 of 2,477 submissions, 30%

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    View all
    • (2025)The Voronoi Diagram of Weakly Smooth Planar Point Sets in $$O(\log n)$$ Deterministic Rounds on the Congested CliqueComputing and Combinatorics10.1007/978-981-96-1093-8_39(478-489)Online publication date: 20-Feb-2025
    • (2024)Boolean Matrix Multiplication for Highly Clustered Data on the Congested CliqueEuro-Par 2024: Parallel Processing10.1007/978-3-031-69583-4_4(45-58)Online publication date: 26-Aug-2024

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