Interval routing in reliability networks

  • Authors:

  • Cyril Gavoille;Martin Nehéz

  • Affiliations:

  • Laboratoire Bordelais de Recherche en Informatique, Université Bordeaux, Talence Cedex, France;Faculty of Informatics and Information Technologies, Slovak University of Technology, Bratislava

  • Venue:
  • Theoretical Computer Science - Foundations of software science and computation structures
  • Year:
  • 2005

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Abstract

In this paper, we consider routing with compact tables in reliability networks. More precisely, we study interval routing on random graphs G(B, p) obtained from a base graph B by independently removing each edge with a failure probability 1 - p. We focus on additive stretched routing for n-node random graphs for which the base B is a square mesh and p = 0.5, that is the percolation model at the critical phase. We show a lower bound of Ω(√log n/(δ+2)) on the number of intervals required per edge for every additive stretch δ≥0. On the other side, our experimental results show that the size of the largest biconnected components is Θ(n0.827), and thus that there exists a trivial shortest-path routing scheme using at most O(n0.827) intervals per edge.The results are extended to random meshes of higher dimension. We show that, asymptotically almost surely, the number of intervals per edge for a random r-dimensional mesh with n nodes is Ω(16-r (δ + 2)1-r r-4(log n)1-1/r), for every additive stretch δ≥0 and for every integral dimension r ∈ [1, log2n].