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

  • Cyril Gavoille
  • Quentin Godfroy
  • Laurent Viennot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7109)

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(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.

Keywords

Weighted Graph Elementary Cycle Graph Metrics Distance Oracle Constant Stretch 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Cyril Gavoille
    • 1
  • Quentin Godfroy
    • 1
  • Laurent Viennot
    • 2
  1. 1.LaBRIUniversity of BordeauxFrance
  2. 2.LIAFAINRIA, University Paris 7France

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