GAVOILLE, Cyril; GODFROY, Quentin; VIENNOT, Laurent

doi:10.1007/978-3-642-25873-2_11

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GAVOILLE, Cyril
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Institut universitaire de France [IUF]

GODFROY, Quentin
Laboratoire Bordelais de Recherche en Informatique [LaBRI]

VIENNOT, Laurent
Networks, Graphs and Algorithms [GANG]

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Ce document a été publié dans

15th International Conference on Principles of Distributed Systems (OPODIS), 15th International Conference on Principles of Distributed Systems (OPODIS), OPODIS'11 - 15th International Conference on Principles of Distributed Systems, 2011-12-13, Toulouse. 2011, vol. 7109, p. 143-158

Springer

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Motivated by multipath routing, we introduce a multi-connected variant of spanners. For that purpose we introduce the $p$-multipath cost between two nodes $u$ and $v$ as the minimum weight of a collection of $p$ internally vertex-disjoint paths between $u$ and $v$. Given a weighted graph $G$, a subgraph $H$ is a $p$-multipath $s$-spanner if for all $u,v$, the $p$-multipath cost between $u$ and $v$ in $H$ is at most $s$ times the $p$-multipath cost in $G$. The $s$ factor is called the stretch. Building upon recent results on fault-tolerant spanners, we show how to build $p$-multipath spanners of constant stretch and of $\tO(n^{1+1/k})$ edges\footnote{Tilde-$O$ notation is similar to Big-$O$ up to poly-logarithmic factors in $n$.}, for fixed parameters $p$ and $k$, $n$ being the number of nodes of the graph. Such spanners can be constructed by a distributed algorithm running in $O(k)$ rounds. Additionally, we give an improved construction for the case $p=k=2$. Our spanner $H$ has $O(n^{3/2})$ edges and the $p$-multipath cost in $H$ between any two node is at most twice the corresponding one in $G$ plus $O(W)$, $W$ being the maximum edge weight.< Réduire

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Node-Disjoint Multipath Spanners and their Relationship with Fault-Tolerant Spanners

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