Implementations of Dijkstra’s Algorithm Based on Multi-Level Buckets

  • Conference paper
Network Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 450))

Abstract

A 2-level bucket data structure [6] has been shown to perform well in a Dijkstra’s algorithm implementation [4]. In this paper we study how the implementation performance depends on the number of bucket levels used. In particular we are interested in the best number of levels to use in practice.

Part of this work was done while the first author was at Computer Science Department, Stanford University, and supported in part by NSF Grant CCR-9307045. The second author was supported by the Department of Defense, with partial support from NSF Award CCR-9357849, with matching funds from IBM, Schlumberger Foundation, Shell Foundation, and Xerox Corporation.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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 (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

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. R. K. Ahuja, K. Mehlhorn, J. B. Orlin, and R. E. Tarjan. Faster Algorithms for the Shortest Path Problem. J. Assoc. Comput. Mach., 37(2):213–223, April 1990

    Article  Google Scholar 

  2. R. E. Bellman. On a Routing Problem. Quart Appl. Math., 16:87–90, 1958

    Google Scholar 

  3. R. Brown. Calandar Queues: A Fast O(l) Priority Queue Implementation for the Simulation Event Set Problem. Comm.ACM, 31:1220–1227, 1988

    Article  Google Scholar 

  4. B. V. Cherkassky, A. V. Goldberg, and T. Radzik. Shortest Paths Algorithms: Theory and Experimental Evaluation. Math. Prog., 73:129–174, 1996

    Google Scholar 

  5. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1990

    Google Scholar 

  6. E. V. Denardo and B. L. Fox. Shortest-Route Methods: 1. Reaching. Pruning, and Buckets. Oper. Res., 27:161–186, 1979

    Article  Google Scholar 

  7. R. B. Dial. Algorithm 360: Shortest Path Forest with Topological Ordering. Comm. ACM, 12:632–633, 1969

    Article  Google Scholar 

  8. E. W. Dijkstra. A Note on Two Problems in Connexion with Graphs. Numer. Math., 1:269–271, 1959

    Article  Google Scholar 

  9. E. A. Dinic. Economical algorithms for finding shortest paths in a network. In Yu.S. Popkov and B.L. Shmulyian, editors, Transportation Modeling Systems, pages 36–44. Institute for System Studies, Moscow, 1978. In Russian

    Google Scholar 

  10. L. R. Ford, Jr. and D. R. Fulkerson. Flows in Networks. Princeton Univ. Press, Princeton, NJ, 1962

    Google Scholar 

  11. M. L. Fredman and R. E. Tarjan. Fibonacci Heaps and Their Uses in Improved Network Optimization Algorithms. J. Assoc. Comput. Mach., 34:596–615, 1987

    Article  Google Scholar 

  12. M. L. Fredman and D. E. Willard. Trans-dichotomous Algorithms for Minimum Spanning Trees and Shortest Paths. J. Comp. and Syst. Sci., 48:533–551, 1994

    Article  Google Scholar 

  13. G. Gallo and S. Pallottino. Shortest Paths Algorithms. Annals of Oper. Res., 13:3–79, 1988

    Article  Google Scholar 

  14. B. Ju. Levit and B. N. Livshits. Nelineinye Setevye Transportnye Zadachi. Transport, Moscow, 1972. In Russian

    Google Scholar 

  15. E. F. Moore. The Shortest Path Through a Maze. In Proc. of the Int. Symp. on the Theory of Switching, pages 285–292. Harvard University Press, 1959

    Google Scholar 

  16. P. Van Emde Boas and R. Kaas and E. Zijlstra. Design and implementation of an efficient priority queue. Math. Systems Theory, 10:99–127, 1977

    Article  Google Scholar 

  17. U. Pape. Implementation and Efficiency of Moore Algorithms for the Shortest Root Problem. Math. Prog., 7:212–222, 1974

    Article  Google Scholar 

  18. R. E. Tarjan. Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983

    Book  Google Scholar 

  19. M. Thorup. On RAM Priority Queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pages 59–67, 1996

    Google Scholar 

  20. R. A. Wagner. A shortest path algorithm for edge-sparse graphs. J. Assoc. Comput. Mach., 23:50–57, 1976

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goldberg, A.V., Silverstein, C. (1997). Implementations of Dijkstra’s Algorithm Based on Multi-Level Buckets. In: Pardalos, P.M., Hearn, D.W., Hager, W.W. (eds) Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59179-2_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59179-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62541-4

  • Online ISBN: 978-3-642-59179-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Navigation