Constant-Round Spanners and Shortest Paths in Congested Clique and MPC

Michal Dory; Orr Fischer; Seri Khoury; Dean Leitersdorf

doi:10.1145/3465084.3467928

Constant-Round Spanners and Shortest Paths in Congested Clique and MPC

Michal Dory, Orr Fischer, Seri Khoury, Dean Leitersdorf

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this work we present the first constant-round algorithms for computing spanners and approximate All-Pairs Shortest Paths (APSP) in the distributed CONGESTED CLIQUE model. Specifically, we show the following results for undirected n-node graphs. ulFor every integer k ≥ 1, O(1)-round algorithms for constructing O(k)-spanners with O(n1+1/k) edges in unweighted graphs, and O(k)-spanners with O(n1+1/k log n) edges in weighted graphs. An O(1)-round algorithm for O(log n)-approximation for APSP in unweighted graphs. An O(1)-round algorithm for O(log2n)-approximation for APSP in weighted graphs. All our algorithms are randomized and succeed with high probability. Prior to our work, the fastest algorithms for computing O(k)-spanners in this model require poly(log k) rounds [Parter, Yogev, DISC '18] [Biswas et al., SPAA '21], and the fastest algorithms for approximate shortest paths require poly(log log n) rounds [Dory, Parter, PODC '20]. Our results extend to the closely related massively parallel computation (MPC) model with near-linear memory per machine, leading to the first O(1)-round algorithms for spanners and approximate shortest paths in this model as well.

Original language	English
Title of host publication	PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing
Publisher	Association for Computing Machinery
Pages	223-233
Number of pages	11
ISBN (Electronic)	9781450385480
DOIs	https://doi.org/10.1145/3465084.3467928
State	Published - 21 Jul 2021
Externally published	Yes
Event	40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021 - Virtual, Online, Italy Duration: 26 Jul 2021 → 30 Jul 2021

Publication series

Name	Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference	40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021
Country/Territory	Italy
City	Virtual, Online
Period	26/07/21 → 30/07/21

Bibliographical note

Publisher Copyright:
© 2021 ACM.

Keywords

congested clique
massively parallel computation
shortest paths
spanners

ASJC Scopus subject areas

Software
Hardware and Architecture
Computer Networks and Communications

Access to Document

10.1145/3465084.3467928

Cite this

Dory, M., Fischer, O., Khoury, S., & Leitersdorf, D. (2021). Constant-Round Spanners and Shortest Paths in Congested Clique and MPC. In PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing (pp. 223-233). (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing). Association for Computing Machinery. https://doi.org/10.1145/3465084.3467928

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abstract = "In this work we present the first constant-round algorithms for computing spanners and approximate All-Pairs Shortest Paths (APSP) in the distributed CONGESTED CLIQUE model. Specifically, we show the following results for undirected n-node graphs. ulFor every integer k ≥ 1, O(1)-round algorithms for constructing O(k)-spanners with O(n1+1/k) edges in unweighted graphs, and O(k)-spanners with O(n1+1/k log n) edges in weighted graphs. An O(1)-round algorithm for O(log n)-approximation for APSP in unweighted graphs. An O(1)-round algorithm for O(log2n)-approximation for APSP in weighted graphs. All our algorithms are randomized and succeed with high probability. Prior to our work, the fastest algorithms for computing O(k)-spanners in this model require poly(log k) rounds [Parter, Yogev, DISC '18] [Biswas et al., SPAA '21], and the fastest algorithms for approximate shortest paths require poly(log log n) rounds [Dory, Parter, PODC '20]. Our results extend to the closely related massively parallel computation (MPC) model with near-linear memory per machine, leading to the first O(1)-round algorithms for spanners and approximate shortest paths in this model as well.",

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Dory, M, Fischer, O, Khoury, S & Leitersdorf, D 2021, Constant-Round Spanners and Shortest Paths in Congested Clique and MPC. in PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing. Proceedings of the Annual ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, pp. 223-233, 40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021, Virtual, Online, Italy, 26/07/21. https://doi.org/10.1145/3465084.3467928

Constant-Round Spanners and Shortest Paths in Congested Clique and MPC. / Dory, Michal; Fischer, Orr; Khoury, Seri et al.
PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery, 2021. p. 223-233 (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Dory M, Fischer O, Khoury S, Leitersdorf D. Constant-Round Spanners and Shortest Paths in Congested Clique and MPC. In PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery. 2021. p. 223-233. (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing). doi: 10.1145/3465084.3467928

Constant-Round Spanners and Shortest Paths in Congested Clique and MPC

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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