Skip to main content
Log in

Formal derivation of graph algorithmic programs using partition-and-recur

  • Special Section Papers
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

In this paper, we derive, by presenting some suitable notations, three typical graph algorithms and corresponding programs using a unified approach, partition-and-recur. We put emphasis on the derivation rather than the algorithms themselves. The main ideas and ingenuity of these algorithms are revealed by formula deduction. Success in these examples gives us more evidence that partition-and-recur is a simple and practical approach and developing enough suitable notations is the key in designing and deriving efficient and correct algorithmic programs.

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

Access this article

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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Xue Jinyun. A unified approach for developing efficient algorithmic programs.Journal of Computer Science and Technology, 1997, 12(4).

  2. Dijkstra E W. A note on two problems connexion with graph.Numer. Math., 1959, 1: 269–271.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bellman R. On a routing problem.Quart. Appl. Math., 1958, 16: 87–90.

    MATH  MathSciNet  Google Scholar 

  4. Cormen T H, Leiserson C E, Rivest R L. Introduction to Algorithms. MIT Press, 1994.

  5. Ford L, Fulkerson D. Flows in Networks. Princeton University Press, 1962.

  6. Backhouse R C, Eijnde J P H W, van Gasteren A J M. Calculating path algorithms.Science of Computer Programming, 1994 22: 3–19.

    Article  MATH  MathSciNet  Google Scholar 

  7. Xue Jinyun. Two new strategies for developing loop invariant and its applications.Journal of Computer Science and Technology, 1993, 8(2).

  8. Xue Jinyun. Program specification and its transformation techniques.Computer and Modernization, April 1993.

  9. Dijkstra E W. A Discipline of Programming. Prentice Hall, New Jersey, 1976.

    MATH  Google Scholar 

  10. Knuth D. A simple program whose proof is not. InBeauty is Our Business. A Birthday Salute to Dijkstra E W. Feijen W H Jet al. (ed.), 1990.

  11. Xue Jinyun, Davis R. A simple program whose derivation and proof is also. InProceedings of The First IEEE International Conference on Formal Engineering Method (ICFEM'97), IEEE CS Press, 1997, 11.

  12. Xue J, Davis R. A derivation and proof of Knuth' binary to decemal, program.Software—Concepts and Tools, 1997, 18: 149–156.

    Google Scholar 

  13. Xue Jinyun. Research on formal development of algorithmic program. InProceedings of National Theoretical Computer Science Conference of China, Journal of Yunnan University, 1997, (19).

  14. Berry D M. Whither Formal Method? Some thoughts on the application of formal methods to the problems of software engineering. InProceedings of Workshop on Increasing the Practical Impact of Formal Methods for Computer-Aided Software Development: Software Evolution, Sept. 1994, pp. 22–37.

  15. Clarke E M, Wing J M. Formal method: State of the art and future directions.ACM Computing Surveys, Dec. 1996, 28(4).

  16. Gries D. The Science of Programming. Springer-Verlag, New York, 1981.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xue Jinyun.

Additional information

This research was supported by National “863” Hi-Tech Programme(Grant No. 863-306-05-07-1) and NNSF (Grant No. 69783006) of China.

Xue Jinyun graduated from Department of Mathematics of Nanjing University in 1970. From Dec. 1985 to April 1988, he worked as a visiting scholar at Cornell University. After June 1995, he spent 10 months as a visiting scholar at Santa Clara University. He is a Professor and the Director of Computer Software Institute at Jiangxi Normal University. His research interests include Cover's theory of algorithms and programs, software engineering and computer-aided instruction.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xue, J. Formal derivation of graph algorithmic programs using partition-and-recur. J. of Comput. Sci. & Technol. 13, 553–561 (1998). https://doi.org/10.1007/BF02946498

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02946498

Keywords

Navigation