Multipath Spanners
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| hal.structure.identifier | Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE] | |
| hal.structure.identifier | Institut universitaire de France [IUF] | |
| dc.contributor.author | GAVOILLE, Cyril | |
| hal.structure.identifier | Laboratoire Bordelais de Recherche en Informatique [LaBRI] | |
| dc.contributor.author | GODFROY, Quentin | |
| hal.structure.identifier | Laboratoire d'informatique Algorithmique : Fondements et Applications [LIAFA] | |
| hal.structure.identifier | Networks, Graphs and Algorithms [GANG] | |
| dc.contributor.author | VIENNOT, Laurent | |
| dc.contributor.editor | Boaz Patt-Shamir, Tinaz Ekim | |
| dc.date.accessioned | 2024-04-15T09:48:10Z | |
| dc.date.available | 2024-04-15T09:48:10Z | |
| dc.date.issued | 2010 | |
| dc.date.conference | 2010-06-07 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/198160 | |
| dc.description.abstractEn | This paper concerns graph spanners that approximate multipaths between pair of vertices of an undirected graphs with $n$ vertices. Classically, a spanner $H$ of stretch $s$ for a graph $G$ is a spanning subgraph such that the distance in $H$ between any two vertices is at most $s$ times the distance in $G$. We study in this paper spanners that approximate short cycles, and more generally $p$ edge-disjoint paths with $p>1$, between any pair of vertices. For every unweighted graph $G$, we construct a $2$-multipath $3$-spanner of $O(n^3/2)$ edges. In other words, for any two vertices $u,v$ of $G$, the length of the shortest cycle (with no edge replication) traversing $u,v$ in the spanner is at most thrice the length of the shortest one in $G$. This construction is shown to be optimal in term of stretch and of size. In a second construction, we produce a $2$-multipath $(2,8)$-spanner of $O(n^3/2)$ edges, i.e., the length of the shortest cycle traversing any two vertices have length at most twice the shortest length in $G$ plus eight. For arbitrary $p$, we observe that, for each integer $k\ge 1$, every weighted graph has a $p$-multipath $p(2k-1)$-spanner with $O(p n^1+1/k)$ edges, leaving open the question whether, with similar size, the stretch of the spanner can be reduced to $2k-1$ for all $p>1$. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | Multipath Spanners | |
| dc.type | Communication dans un congrès | |
| dc.identifier.doi | 10.1007/978-3-642-13284-1_17 | |
| dc.subject.hal | Informatique [cs]/Calcul parallèle, distribué et partagé [cs.DC] | |
| dc.subject.hal | Informatique [cs]/Réseaux et télécommunications [cs.NI] | |
| bordeaux.page | 211-223 | |
| bordeaux.volume | 6058 | |
| bordeaux.hal.laboratories | Laboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | Structural Information and Communication Complexity, 17th International Colloquium (SIROCCO) | |
| bordeaux.country | TR | |
| bordeaux.conference.city | Sirince | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00547869 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.conference.end | 2010-06-11 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00547869v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2010&rft.volume=6058&rft.spage=211-223&rft.epage=211-223&rft.au=GAVOILLE,%20Cyril&GODFROY,%20Quentin&VIENNOT,%20Laurent&rft.genre=unknown |
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