On the robustness of interconnections in random graphs: a symbolic approach

  • Authors:

  • P. Flajolet;K. Hatzis;S. Nikoletseas;P. Spirakis

  • Affiliations:

  • Algorithms Project, INRIA Rocquencourt, France;Computer Technology Institute (CTI), P.O. Box 1122, Riga Fereou 61, 26110, Patras, Greece and Computer Engineering and Informatics Department, Patras University, Greece;Computer Technology Institute (CTI), P.O. Box 1122, Riga Fereou 61, 26110, Patras, Greece and Computer Engineering and Informatics Department, Patras University, Greece;Computer Technology Institute (CTI), P.O. Box 1122, Riga Fereou 61, 26110, Patras, Greece and Computer Engineering and Informatics Department, Patras University, Greece

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2002

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Abstract

Graphs are models of communication networks. This paper applies symbolic combinatorial techniques in order to characterize the interplay between two parameters of a random graph, namely its density (the number of edges in the graph) and its robustness to link failures. Here, robustness means multiple connectivity by short disjoint paths: a triple (G,s,t), where G is a graph and s, t are designated vertices, is called l-robust if s and t are connected via at least two edge-disjoint paths of length at most l. We determine the expected number of ways to get from s to t via two edge-disjoint paths of length l in the classical random graph model gn.p by means of "symbolic" combinatorial methods. We then derive bounds on related threshold probabilities as functions of l and n.