On the Locality of Distributed Sparse Spanner Construction
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| dc.contributor.author | DERBEL, Bilel | |
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| hal.structure.identifier | Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE] | |
| dc.contributor.author | GAVOILLE, Cyril | |
| hal.structure.identifier | Department of Computer Science and Applied Mathematics [Rehovot] | |
| dc.contributor.author | PELEG, David | |
| hal.structure.identifier | Networks, Graphs and Algorithms [GANG] | |
| dc.contributor.author | VIENNOT, Laurent | |
| dc.date.accessioned | 2024-04-15T09:51:33Z | |
| dc.date.available | 2024-04-15T09:51:33Z | |
| dc.date.created | 2008 | |
| dc.date.issued | 2008-02 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/198438 | |
| dc.description | Rapport de recherche | |
| dc.description.abstractEn | The paper presents a deterministic distributed algorithm that, given k>0, constructs in k rounds a (2k-1,0)-spanner of O(k n^{1+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(k n^{1+1/k}) edges.) Previous distributed solutions achieving such optimal stretch-size trade-off either make use of randomization and provide no performance guarantees, or perform in log^{Omega(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 eps>0, constructs a (1+eps,2)-spanner of O(eps^{-2} n^{3/2}) edges in O(eps^{-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)}) edges for k in {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 + eps} edges in at most n^{eps} expected rounds must stretch some distances by an additive factor of n^{Omega(eps)}. In other words, 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 polynomial number of rounds in expectation. | |
| dc.language.iso | en | |
| dc.title.en | On the Locality of Distributed Sparse Spanner Construction | |
| dc.type | Autre document | |
| dc.subject.hal | Informatique [cs]/Mathématique discrète [cs.DM] | |
| bordeaux.hal.laboratories | Laboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00400407 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| dc.subject.it | spanner | |
| dc.subject.it | distributed | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00400407v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2008-02&rft.au=DERBEL,%20Bilel&GAVOILLE,%20Cyril&PELEG,%20David&VIENNOT,%20Laurent&rft.genre=unknown |
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