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On the Locality of Distributed Sparse Spanner Construction

hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
dc.contributor.authorDERBEL, Bilel
hal.structure.identifierLaboratoire Bordelais de Recherche en Informatique [LaBRI]
hal.structure.identifierAlgorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
dc.contributor.authorGAVOILLE, Cyril
hal.structure.identifierDepartment of Computer Science and Applied Mathematics [Rehovot]
dc.contributor.authorPELEG, David
hal.structure.identifierNetworks, Graphs and Algorithms [GANG]
dc.contributor.authorVIENNOT, Laurent
dc.date.accessioned2024-04-15T09:51:33Z
dc.date.available2024-04-15T09:51:33Z
dc.date.created2008
dc.date.issued2008-02
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/198438
dc.descriptionRapport de recherche
dc.description.abstractEnThe 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.isoen
dc.title.enOn the Locality of Distributed Sparse Spanner Construction
dc.typeAutre document
dc.subject.halInformatique [cs]/Mathématique discrète [cs.DM]
bordeaux.hal.laboratoriesLaboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00400407
hal.version1
hal.popularnon
hal.audienceNon spécifiée
dc.subject.itspanner
dc.subject.itdistributed
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00400407v1
bordeaux.COinSctx_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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