TY - GEN

T1 - Constant-Round Near-Optimal Spanners in Congested Clique

AU - Chechik, Shiri

AU - Zhang, Tianyi

N1 - Publisher Copyright:
© 2022 ACM.

PY - 2022/7/20

Y1 - 2022/7/20

N2 - Graph spanners have been extensively studied in the literature of graph algorithms. In an undirected weighted graph G = (V, E,ω) on n vertices, a t-spanner of G is a subgraph that preserves pairwise distances up to a multiplicative stretch factor of t . It is well-known that, for any integer k, a (2k - 1)-spanner with O(n1+1/k ) edges always exists, and the stretch-sparsity balance is tight under the girth conjecture by Erdos. In this paper, we are interested in efficient algorithms for spanners in the distributed setting. Specifically, we present constant-round congested clique algorithms for spanners with nearly optimal stretch-sparsity trade-offs: (2k-1)-spanners with O(n1+1/k ) edges in unweighted graphs (i.e. ω 1). (1 + ) (2k - 1)-spanners with O(n1+1/k ) edges in weighted graphs. (2k-1)-spanners withO(kn1+1/k ) edges in weighted graphs.

AB - Graph spanners have been extensively studied in the literature of graph algorithms. In an undirected weighted graph G = (V, E,ω) on n vertices, a t-spanner of G is a subgraph that preserves pairwise distances up to a multiplicative stretch factor of t . It is well-known that, for any integer k, a (2k - 1)-spanner with O(n1+1/k ) edges always exists, and the stretch-sparsity balance is tight under the girth conjecture by Erdos. In this paper, we are interested in efficient algorithms for spanners in the distributed setting. Specifically, we present constant-round congested clique algorithms for spanners with nearly optimal stretch-sparsity trade-offs: (2k-1)-spanners with O(n1+1/k ) edges in unweighted graphs (i.e. ω 1). (1 + ) (2k - 1)-spanners with O(n1+1/k ) edges in weighted graphs. (2k-1)-spanners withO(kn1+1/k ) edges in weighted graphs.

KW - congested clique

KW - shortest paths

KW - spanners

UR - http://www.scopus.com/inward/record.url?scp=85135322836&partnerID=8YFLogxK

U2 - 10.1145/3519270.3538439

DO - 10.1145/3519270.3538439

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AN - SCOPUS:85135322836

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

SP - 325

EP - 334

BT - PODC 2022 - Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 41st ACM Symposium on Principles of Distributed Computing, PODC 2022

Y2 - 25 July 2022 through 29 July 2022

ER -