Skip to main content
Springer Nature Link
Log in

Calculating a Relational Program for Transitive Reductions of Strongly Connected Graphs

  • Conference paper
  • First Online:
Relational Methods in Computer Science (RelMiCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2561))

Included in the following conference series:

  • 325 Accesses

Abstract

Based on a generic program for computing minimal sets, we present a simple relational program for computing transitive reductions of strongly connected directed graphs. It uses a precomputation phase and can easily be implemented in quadratic running time. The presentation is done as an exercise in generic programming and for combining the Dijkstra-Gries method and relational algebra to derive graph algorithms.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aho A. V., Hopcroft J. E., Ullman J. D.: The design and analysis of computer algorithms. Addison-Wesley (1974).

    Google Scholar 

  2. Behnke R. et al.: Applications of the Rel View system. In: Berghammer R., Lakhnech Y. (eds.): Tool support for system specification, development and verification. Advances in Computing, Springer, 33–47 (1999).

    Google Scholar 

  3. Berghammer R., Hoffmann T.: Relational depth-first-search with applications. In: Desharnais J. (ed.): Proc. 5th Int. Seminar on Relational Methods in Computer Science, Laval Univ., Dept. d’Informatique, 11–20 (2000). Extended version in: Information Sciences 139, 167–186 (2001).

    Google Scholar 

  4. Berghammer R.: Combining relational calculus and the Dijkstra-Gries method for deriving relational programs. Information Sciences 119, 155–171 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  5. Cormen T. H., Leiserson C. E., Rivest R. L.: Introduction to algorithms. The MIT Press (1990).

    Google Scholar 

  6. Dijkstra E. W.: A discipline of programming. Prentice-Hall (1976).

    Google Scholar 

  7. Gries D.: The science of computer programming. Springer (1981).

    Google Scholar 

  8. Hoffmann T.: Case studies in relational program development by selected strategies for graph searching (in German). Ph.D. thesis, Institut für Informatik und Praktische Mathematik, Universität Kiel (2002).

    Google Scholar 

  9. Kasper C.: Investigating algorithms for transitive reductions and minimum equivalent digraphs (in German). Diploma thesis, Institut für Informatik und Praktische Mathematik, Universität Kiel (2001).

    Google Scholar 

  10. Khuller S., Raghavachari B., Young N.: Approximating the minimum equivalent digraph. SIAM Journal on Computing 24, 859–972 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  11. Noltemeier H.: Reduktion von Präzedenzstrukturen. Zeitschrift für Operations Res. 20, 151–159 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  12. Ravelo J.: Two graph algorithms derived. Acta Informatica 36, 489–510 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  13. Schmidt G., Ströhlein T.: Relations and graphs. Springer (1993).

    Google Scholar 

  14. Simon K.: Finding a minimal transitive reduction in a strongly connected digraph within linear time. In: Nagl M. (ed.): Proc. 15th Workshop on Graph-Theoretic Concepts in Computer Science, LNCS 411, Springer, 245–259 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität Kiel, Olshausenstraβe 40, D-24098, Kiel

    Rudolf Berghammer & Thorsten Hoffmann

Authors
  1. Rudolf Berghammer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thorsten Hoffmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Tilburg University, P.O. Box 90153, 5000, LE Tilburg, The Netherlands

    Harrie C. M. de Swart

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Berghammer, R., Hoffmann, T. (2002). Calculating a Relational Program for Transitive Reductions of Strongly Connected Graphs. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_18

Download citation

  • DOI: https://doi.org/10.1007/3-540-36280-0_18

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00315-1

  • Online ISBN: 978-3-540-36280-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics