Congested Clique Algorithms for Graph Spanners

Authors Merav Parter, Eylon Yogev

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Author Details

Merav Parter
  • Weizmann IS, Rehovot, Israel
Eylon Yogev
  • Weizmann IS, Rehovot, Israel

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Merav Parter and Eylon Yogev. Congested Clique Algorithms for Graph Spanners. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling schemes and routing to solving linear systems and spectral sparsification. A k-spanner maintains pairwise distances up to multiplicative factor of k. It is a folklore that for every n-vertex graph G, one can construct a (2k-1) spanner with O(n^{1+1/k}) edges. In a distributed setting, such spanners can be constructed in the standard CONGEST model using O(k^2) rounds, when randomization is allowed. In this work, we consider spanner constructions in the congested clique model, and show: - a randomized construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k) rounds. The previous best algorithm runs in O(k) rounds; - a deterministic construction of a (2k-1)-spanner with O~(n^{1+1/k}) edges in O(log k +(log log n)^3) rounds. The previous best algorithm runs in O(k log n) rounds. This improvement is achieved by a new derandomization theorem for hitting sets which might be of independent interest; - a deterministic construction of a O(k)-spanner with O(k * n^{1+1/k}) edges in O(log k) rounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Distributed Graph Algorithms
  • Spanner
  • Congested Clique


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