TY - GEN

T1 - Constant-Round Spanners and Shortest Paths in Congested Clique and MPC

AU - Dory, Michal

AU - Fischer, Orr

AU - Khoury, Seri

AU - Leitersdorf, Dean

N1 - Publisher Copyright:
© 2021 ACM.

PY - 2021/7/21

Y1 - 2021/7/21

N2 - 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.

AB - 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.

KW - congested clique

KW - massively parallel computation

KW - shortest paths

KW - spanners

UR - http://www.scopus.com/inward/record.url?scp=85112389386&partnerID=8YFLogxK

U2 - 10.1145/3465084.3467928

DO - 10.1145/3465084.3467928

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AN - SCOPUS:85112389386

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 223

EP - 233

BT - PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021

Y2 - 26 July 2021 through 30 July 2021

ER -