Network Verification via Routing Table Queries

  • Evangelos Bampas
  • Davide Bilò
  • Guido Drovandi
  • Luciano Gualà
  • Ralf Klasing
  • Guido Proietti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6796)

Abstract

We address the problem of verifying the accuracy of a map of a network by making as few measurements as possible on its nodes. This task can be formalized as an optimization problem that, given a graph G = (V,E), and a query model specifying the information returned by a query at a node, asks for finding a minimum-size subset of nodes of G to be queried so as to univocally identify G. This problem has been faced w.r.t. a couple of query models assuming that a node had some global knowledge about the network. Here, we propose a new query model based on the local knowledge a node instead usually has. Quite naturally, we assume that a query at a given node returns the associated routing table, i.e., a set of entries which provides, for each destination node, a corresponding (set of) first-hop node(s) along an underlying shortest path. First, we show that any network of n nodes needs Ω(loglogn) queries to be verified. Then, we prove that there is no o(logn)-approximation algorithm for the problem, unless \(\mbox{\sf P}=\mbox{\sf NP}\), even for networks of diameter 2. On the positive side, we provide an O(logn)-approximation algorithm to verify a network of diameter 2, and we give exact polynomial-time algorithms for paths, trees, and cycles of even length.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Evangelos Bampas
    • 1
  • Davide Bilò
    • 2
  • Guido Drovandi
    • 3
  • Luciano Gualà
    • 4
  • Ralf Klasing
    • 1
  • Guido Proietti
    • 3
    • 5
  1. 1.LaBRI, CNRS / INRIA / University of BordeauxBordeauxFrance
  2. 2.Dip. di Teorie e Ricerche dei Sistemi CulturaliUniversity of SassariItaly
  3. 3.Istituto di Analisi dei Sistemi ed Informatica, CNRRomeItaly
  4. 4.Dipartimento di MatematicaUniversity of Tor VergataRomeItaly
  5. 5.Dipartimento di InformaticaUniversity of L’AquilaL’AquilaItaly

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