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Constant-Round Near-Optimal Spanners in Congested Clique

Published: 21 July 2022 Publication History

Abstract

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 + ε) (2k - 1)-spanners with O(n1+1/k ) edges in weighted graphs. (2k-1)-spanners withO(kn1+1/k ) edges in weighted graphs.

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References

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cover image ACM Conferences
PODC'22: Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
July 2022
509 pages
ISBN:9781450392624
DOI:10.1145/3519270
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Published: 21 July 2022

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  1. congested clique
  2. shortest paths
  3. spanners

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