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Sparse Hopsets in Congested Clique

Author Yasamin Nazari

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Yasamin Nazari
  • Johns Hopkins University, Baltimore, MD, United States


The author would like to thank Michael Dinitz and Goran Zuzic for helpful discussions.

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Yasamin Nazari. Sparse Hopsets in Congested Clique. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 34:1-34:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


We give the first Congested Clique algorithm that computes a sparse hopset with polylogarithmic hopbound in polylogarithmic time. Given a graph G=(V,E), a (β,ε)-hopset H with "hopbound" β, is a set of edges added to G such that for any pair of nodes u and v in G there is a path with at most β hops in G ∪ H with length within (1+ε) of the shortest path between u and v in G. Our hopsets are significantly sparser than the recent construction of [Censor-Hillel et al., 2019], that constructs a hopset of size Õ (n^{3/2}), but with a smaller polylogarithmic hopbound. On the other hand, the previously known construction of sparse hopsets with polylogarithmic hopbound in the Congested Clique model, proposed by [Elkin and Neiman, 2018; Elkin and Neiman, 2019; Elkin and Neiman, 2019], all require polynomial rounds. One tool that we use is an efficient algorithm that constructs an l-limited neighborhood cover, that may be of independent interest. Finally, as a side result, we also give a hopset construction in a variant of the low-memory Massively Parallel Computation model, with improved running time over existing algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Hopsets
  • Congested Clique
  • Shortest Paths
  • Massively Parallel Computation


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