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Survivable Networks with Bounded Delay: The Edge Failure Case

(Extended Abstract)

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Algorithms and Computation (ISAAC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1741))

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Abstract

We introduce new classes of graphs to investigate networks that guarantee constant delays even in the case of multiple edge failures. This means the following: as long as two vertices remain connected if some edges have failed, then the distance between these vertices in the faulty graph is at most a constant factor k times the original distance. In this extended abstract, we consider the case where the number of edge failures is bounded by a constant l. These graphs are called (k, l)- self-spanners. We prove that the problem of maximizing l for a given graph when k > 4 is fixed is NP-complete, whereas the dual problem of minimizing k when l is fixed is solvable in polynomial time.We show how the Cartesian product affects the self-spanner properties of the composed graph. As a consequence, several popular network topologies (like grids, tori, hypercubes, butterflies, and cube-connected cycles) are investigated with respect to their self-spanner properties.

Research partially supported by Italian MURST project ‘Teoria dei Grafie e Appli- cazioni’, and by the Deutsche Forschungsgemeinschaft under grant Wa 65410-2

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Authors and Affiliations

  1. Dipartemento di Ingegneria Elettrica, Università degli Studi di L’Aquila, I-67040 Monteluco di Roio, L’Aquila, Italy

    Serafino Cicerone & Gabriele Di Stefano

  2. Fakultät für Mathematik und Informatik, Universität Konstanz, 78457, Konstanz, Germany

    Dagmar Handke

Authors
  1. Serafino Cicerone
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  2. Gabriele Di Stefano
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  3. Dagmar Handke
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© 1999 Springer-Verlag Berlin Heidelberg

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Cicerone, S., Stefano, G.D., Handke, D. (1999). Survivable Networks with Bounded Delay: The Edge Failure Case. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_22

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  • DOI: https://doi.org/10.1007/3-540-46632-0_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66916-6

  • Online ISBN: 978-3-540-46632-1

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