Survivable Networks with Bounded Delay: The Edge Failure Case

(Extended Abstract)
  • Serafino Cicerone
  • Gabriele Di Stefano
  • Dagmar Handke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)


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.


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  1. 1.
    F. S. Annexstein. Fault tolerance in hypercube-derivative networks. Computer Architecture News, 19(1):25–34, 1991.CrossRefMathSciNetGoogle Scholar
  2. 2.
    F. S. Annexstein, M. Baumslag, and A. L. Rosenberg. Group action graphs and parallel architectures. SIAM J. Comput., 19(3):544–569, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    J. Bruck, R. Cypher, and C.-T. Ho. Fault-tolerant meshes with small degree. SIAM J. Comput., 26(6):1764–1784, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    S. Cicerone and G. Di Stefano. Graphs with bounded induced distance. In Proceedings 24th International Workshop on Graph-Theoretic Concepts in Computer Science, WG’98, pages 177–191. Springer-Verlag, Lecture Notes in Computer Science, vol. 1517, 1998.Google Scholar
  5. 5.
    S. Cicerone, G. Di Stefano, and D. Handke. Survivable Networks with Bounded Delays. Technical Report, Konstanzer Schriften in Mathematik und Informatik n. 81, University of Konstanz, Germany, February 1999.Google Scholar
  6. 6.
    R. Cole, B. M. Maggs, and R. K. Sitaraman. Reconfiguring arrays with faults part I: Worst-case faults. SIAM J. Comput., 26(6):1581–1611, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP Completeness. W H Freeman & Co Ltd, 1979.Google Scholar
  8. 8.
    D. Handke. Independent tree spanners: Fault-tolerant spanning trees with constant distance guarantees (extended abstract). In Proceedings 24th International Workshop on Graph-Theoretic Concepts in Computer Science, WG’98, pages 203–214. Springer-Verlag, Lecture Notes in Computer Science, vol. 1517, 1998.Google Scholar
  9. 9.
    M.-C. Heydemann, J. G. Peters, and D. Sotteau. Spanners of hypercube-derived networks. SIAM J. on Discr. Math., 9(1):37–54, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    A. Itai, Y. Perl, and Y. Shiloach. The complexity of finding maximum disjoint paths with length constraints. Networks, 12:277–286, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    F. T. Leighton. Introduction to parallel algorithms and architectures: arrays, trees, hypercubes. Morgan Kaufman Publishers, 1992.Google Scholar
  12. 12.
    F. T. Leighton, B. M. Maggs, and R. K. Sitaraman. On the fault tolerance of some popular bounded-degree networks. SIAM J. Comput., 27(6):1303–1333, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    D. Peleg and A. A. Schäffer. Graph spanners. J. of Graph Theory, 13:99–116, 1989.zbMATHCrossRefGoogle Scholar
  14. 14.
    A. L. Rosenberg. Cycles in networks. Technical Report UM-CS-1991-020, Dept. of Computer and Information Science, Univ. of Massachusetts, 1991.Google Scholar
  15. 15.
    T.-Y. Sung, M.-Y. Lin, and T.-Y. Ho. Multiple-edge-fault tolerance with respect to hypercubes. IEEE Trans. Parallel and Distributed Systems, 8(2):187–192, 1997.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Serafino Cicerone
    • 1
  • Gabriele Di Stefano
    • 1
  • Dagmar Handke
    • 2
  1. 1.Dipartemento di Ingegneria ElettricaUniversità degli Studi di L’AquilaI-67040 Monteluco di RoioItaly
  2. 2.Fakultät für Mathematik und InformatikUniversität KonstanzKonstanzGermany

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