On the locality of distributed sparse spanner construction

Bilel Derbel, Cyril Gavoille, David Peleg, Laurent Viennot

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

40 Scopus citations


The paper presents a deterministic distributed algorithm that, given k ≥ 1, constructs in k rounds a (2k-1, 0)-spanner of O(kn1+1/k) edges for every n-node unweighted graph, (If n is not available to the nodes, then our algorithm executes in 3k - 2 rounds, and still returns a (2k - 1, 0)-spanner with O(kn1+1/k) edges.) Previous distributed solutions achieving such optimal stretch-size trade-off either make use of randomization providing performance guarantees in expectation only, or perform in log Ω(1) n rounds, and all require a priori knowledge of n. Based on this algorithm, we propose a second deterministic distributed algorithm that, for every ∈ > 0, constructs a (1 + ∈, 2)-spanner of O(∈-1n3/2) edges in O(∈-1) rounds, without any prior knowledge on the graph. Our algorithms are complemented with lower bounds, which hold even under the assumption that n is known to the nodes. It is shown that any (randomized) distributed algorithm requires k rounds in expectation to compute a (2k - 1, 0)-spanner of o(n1+1/(k-1)) edges for k ∈ {2, 3, 5}. It is also shown that for every k > 1, any (randomized) distributed algorithm that constructs a spanner with fewer than n1+1/k+∈ edges in at most n expected rounds must stretch some distances by an additive factor of n Ω(∈). In other words, while additive stretched spanners with O(n1+1/k) edges may exist, e.g., for k = 2, 3, they cannot be computed distributively in a sub-polynomial number of rounds in expectation.

Original languageEnglish
Title of host publicationPODC'08
Subtitle of host publicationProceedings of the 27th Annual ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery (ACM)
Number of pages10
ISBN (Print)9781595939890
StatePublished - 2008
Externally publishedYes
Event27th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing - Toronto, ON, Canada
Duration: 18 Aug 200821 Aug 2008

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference27th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing
CityToronto, ON


  • Distributed algorithms
  • Graph spanners
  • Time complexity


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