Distributed computing of efficient routing schemes in generalized chordal graphs

  • Authors:

  • Nicolas Nisse;Ivan Rapaport;Karol Suchan

  • Affiliations:

  • MASCOTTE, INRIA, I3S, CNRS, UNS, Sophia Antipolis, France;DIM, CMM (UMI 2807 CNRS), Universidad de Chile, Santiago, Chile;Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile and WMS, AGH - University of Science and Technology, Cracow, Poland

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2012

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Abstract

Efficient algorithms for computing routing tables should take advantage of particular properties arising in large scale networks. Two of them are of special interest: low (logarithmic) diameter and high clustering coefficient. High clustering coefficient implies the existence of few large induced cycles. Considering this fact, we propose here a routing scheme that computes short routes in the class of k-chordal graphs, i.e., graphs with no induced cycles of length more than k. In the class of k-chordal graphs, our routing scheme achieves an additive stretch of at most k-1, i.e., for all pairs of nodes, the length of the route never exceeds their distance plus k-1. In order to compute the routing tables of any n-node graph with diameter D we propose a distributed algorithm which uses O(logn)-bit messages and takes O(D) time. The corresponding routing scheme achieves the stretch of k-1 on k-chordal graphs. We then propose a routing scheme that achieves a better additive stretch of 1 in chordal graphs (notice that chordal graphs are 3-chordal graphs). In this case, distributed computation of routing tables takes O(min{@DD,n}) time, where @D is the maximum degree of the graph. Our routing schemes use addresses of size logn bits and local memory of size 2(d-1)logn bits per node of degree d.