On the locality of distributed sparse spanner construction

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On the locality of distributed sparse spanner construction (2008)

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by Bilel Derbel , Cyril Gavoille , Laurent Viennot , David Peleg

Venue:	In ACM Press, editor, 27th Annual ACM Symp. on Principles of Distributed Computing (PODC
Citations:	17 - 6 self

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@INPROCEEDINGS{Derbel08onthe,
    author = {Bilel Derbel and Cyril Gavoille and Laurent Viennot and David Peleg},
    title = {On the locality of distributed sparse spanner construction},
    booktitle = {In ACM Press, editor, 27th Annual ACM Symp. on Principles of Distributed Computing (PODC},
    year = {2008},
    pages = {273--282}
}

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Abstract

The paper presents a deterministic distributed algorithm that, given k � 1, constructs in k rounds a (2k−1, 0)-spanner of O(kn 1+1/k)edgesforeveryn-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(kn 1+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 ɛ>0, constructs a (1 + ɛ, 2)-spanner of O(ɛ −1 n 3/2)edgesin O(ɛ −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(n 1+1/(k−1))edgesfork ∈{2, 3, 5}. It is also shown that for every k>1, any (randomized) distributed algorithm that constructs a spanner with fewer than n 1+1/k+ɛ edges in at most n ɛ expected rounds must stretch some distances by an additive factor of n Ω(ɛ).Inotherwords, while additive stretched spanners with O(n 1+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. Supported by the équipe-projet INRIA “DOLPHIN”. Supported by the ANR-project “ALADDIN”, and the

Keyphrases

distributed sparse spanner construction priori knowledge anr-project aladdin optimal stretch-size trade-off performance guarantee quipe-projet inria dolphin prior knowledge sub-polynomial number additive factor edgesforeveryn-node unweighted graph

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