Node-Disjoint multipath spanners and their relationship with fault-tolerant spanners

  • Authors:

  • Cyril Gavoille;Quentin Godfroy;Laurent Viennot

  • Affiliations:

  • LaBRI, University of Bordeaux, France;LaBRI, University of Bordeaux, France;LIAFA, INRIA, University Paris 7, France

  • Venue:
  • OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
  • Year:
  • 2011

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Abstract

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 ${\tilde{O}}(n^{1+1/k})$ edges, 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(n3/2) 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.