Skip to main content
SpringerLink
Log in

Graph rewriting systems and their application to network reliability analysis

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 570))

Included in the following conference series:

  • 252 Accesses

Abstract

We propose a new kind of Graph Rewriting Systems (GRS) that provide a theoretical foundation for using the reduction methods to analyze network reliability, and give the critical pair lemma in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnborg, S., Courcelle, B., Proskurowski, A. and Seese, D.: “An Algebraic Theory of Graph Reduction,” Research Report n° 91–36, Bordeaux-I University, 1991.

    Google Scholar 

  2. Ball, M. O.: “Complexity of Network Reliability Computations,” Networks, Vol. 10, pp. 153–165, 1980.

    Google Scholar 

  3. Barendreght, H.P.: “The Lambda Calculus-Its Syntax and Semantics,” Revised Edition, North Holland, 1984.

    Google Scholar 

  4. Bauderon, Y. and Courcelle, B.: “Graph Expression and Graph Rewritings,” Mathematical Systems Theory, 20, pp. 83–127, 1987.

    Article  Google Scholar 

  5. Brandenburg, F.J.: “On context-free graph grammars with bounded degrees” Proceedings of Toyohashi Symposium on Theoretical Computer Science, pp. 23–26 August, 1990.

    Google Scholar 

  6. Courcelle, B.: “An axiomatic definition of context-free rewriting systems and its application to NLC graph grammars.” Theoretical Computer Science, 55, pp. 141–181, 1987.

    Article  Google Scholar 

  7. Courcelle, B.: “The monadic second order logic of graphs VI: On several presentations of graphs by relational structures.” Research Report n° 89–99, Bordeaux-I University, 1989.

    Google Scholar 

  8. Ehrig, H., Pfender, M., and Schnider, H.: “Graph Grammars: An algebraic approach,” Proceeding 14th IEEE Symposium Switching and Automata Theory, Iowa City, pp. 167–180, 1973.

    Google Scholar 

  9. Ehrig, H.: “Introduction to the algebraic theory of graphs grammars (A Survry),” in Proceeding of 1st International Workshop on Graph Grammars, Lecture Notes Computer Science, Vol. 73, Springer Verlag, Berlin, pp. 1–69, 1979.

    Google Scholar 

  10. Ehrig, H., Kreowski, H.J., Maggiolo-Shettini, A., Rosen, B. R., and Winkowski, J.: “Transformations of structures: an algebraic approach,” Mathematical Systems Theory, Vol 14, pp. 305–334, 1981.

    Google Scholar 

  11. Harary, F.: “Graph Theory,” Addison-Wesley, Reading, MA 1969.

    Google Scholar 

  12. Hayashi, M. and Okada, Y.: “The Equality of Graphs by Reduction Method and Application,” IEICE Japan Tech. Rep. CAS and VLD 90-53, pp. 37–44, 1990.

    Google Scholar 

  13. Hindley, J. and Seldin, J: “Introduction to Combinators and Lambda Calculus,” London Mathematical Society Student Texts 1, Cambridge University, 1986.

    Google Scholar 

  14. Huet, G.P.: “Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems,” Journal of the Association for Computing Machinery, Vol. 27, No. 4, pp. 11–21, 1980.

    Google Scholar 

  15. Knuth, D.E. and Bendix, P.B.: “Simple Word Problems in Universal Algebras,” Computational prŌblems in abstract algebras, Pergamon Press, Oxford 1970.

    Google Scholar 

  16. Le Chenadec, P.: “Canonical Forms in Finitely Presented Algebra,” Research Notes in Theoretical Computer Science, Pitman London, 1986.

    Google Scholar 

  17. Litovsky, I. and Metivier, Y.: “Computing Trees with Graph Rewriting Systems with Priorities,” Research Report n° 90-87, Bordeaux-I University, 1990.

    Google Scholar 

  18. Maggiolo-Schettini, A. and Winkowski, J.: “Process of Transforming Structures” Journal of Computer and System Sciences 24, pp. 245–282, 1982.

    Google Scholar 

  19. Khan, N.M., Rajamani, K. and Banerjee, S.K.: “A direct method to Calculate the Frequency and Duration of Failures for Large Networks,” IEEE Transactions on Reliability Analysis, Vol. R-26, No. 5, December pp.318–321, 1977.

    Google Scholar 

  20. Billaud, M., Lafon, P., Metivier, E. and Sopena, E.: “Graph Rewriting Systems with Priorities,” 15th International Workshop WG, Lecture Note in Computer Science 411, pp. 94–106, 1989.

    Google Scholar 

  21. Newman, M.H.A.: “On theories with a combinatorial definition of ‘equivalence',” Ann. Math., Vol. 43, No. 2, pp. 223–243, 1942.

    Google Scholar 

  22. Okada, Y. and M, Hayashi.: “Graph Rewriting Systems and Application to Network Reliability Analysis.” IEICE Japan Tech. Rep. Comp 90-7, pp. 57–66, 1990.

    Google Scholar 

  23. Politof, T.: ”δ-Y reducible graphs,” Working Paper 88-12-52, Department of Decision Science and Management Information Systems,” Concordia University (May 1989).

    Google Scholar 

  24. Politof, T. and Satyanarayana, A.: “Efficient Algorithms for Reliability Analysis of Planar Networks — A survey,” IEEE Transactions Reliability, Vol. R-35, No. 3, pp. 252–259, August, 1986.

    Google Scholar 

  25. Politof, T. and Satyanarayana, A.: “Network Reliability and Inner-Four-Cycle-Free Graph,” Mathematics of Operation Research, Vol. 11, No. 3, pp. 484–505, August, 1986.

    Google Scholar 

  26. Politof, T. and Satyanarayana, A.: ”A linear time Algorithm to Compute the Reliability of Planar Cube-Free Networks,” IEEE Transactions on Reliability, Vol. R-39, pp. 557–563, Dec, 1990.

    Google Scholar 

  27. Rosenthal, A.: “Computing The Reliability of Complex Networks SIAMJ. APPL. MATH. Vol. 32, No. 2, March, 1977.

    Google Scholar 

  28. Rosenthal, A. and Frisque, D.: “Transformations for Simplifying Network Reliability Calculations” Networks, Vol. 7, pp. 97–111, 1977.

    Google Scholar 

  29. Satyanarayana, A. and Chan, M.: “Network Reliability and the Factoring Theorem,” Networks, Vol. 13, pp. 107–120, 1983.

    Google Scholar 

  30. Satyanarayana, A. and Wood, R. K.: “A Linear-Time Algorithm for computing K-terminal reliability of normal graphs in series-parallel networks,” SIAM J. Computing, Vol. 14, November, 1985.

    Google Scholar 

  31. Sethi, R.: “Testing for the Church-Rosser theorems,” J.ACM, Vol. 21, No. 4, pp. 671–679, October, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NTT Basic Research Lab., NTT Telecommunication Networks Research Lab., 3-9-11, Midori-cho, Musashino, 180, Tokyo, Japan

    Yasuyoshi Okada & Masahiro Hayashi

Authors
  1. Yasuyoshi Okada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masahiro Hayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Gunther Schmidt Rudolf Berghammer

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Okada, Y., Hayashi, M. (1992). Graph rewriting systems and their application to network reliability analysis. In: Schmidt, G., Berghammer, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 1991. Lecture Notes in Computer Science, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55121-2_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-55121-2_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55121-8

  • Online ISBN: 978-3-540-46735-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation