Skip to main content

Shortest Path Algorithms: Engineering Aspects

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

Included in the following conference series:

Abstract

We review shortest path algorithms based on the multi-level bucket data structure [6] and discuss the interplayb etween theorya nd engineering choices that leads to efficient implementations. Our experimental results suggest that the caliber heuristic [17] and adaptive parameter selection give an efficient algorithm, both on typical and on hard inputs, for a wide range of arc lengths.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping 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.

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  MathSciNet  MATH  Google Scholar 

  2. P. Van Emde Boas, R. Kaas, and E. Zijlstra. Design and Implementation of an Efficient PriorityQ ueue. Math. Systems Theory, 10:99–127, 1977.

    Article  MATH  Google Scholar 

  3. B. V. Cherkassky and A. V. Goldberg. Negative-Cycle Detection Algorithms. Math. Prog., 85:277–311, 1999.

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  5. B. V. Cherkassky, A. V. Goldberg, and C. Silverstein. Buckets, Heaps, Lists, and Monotone Priority Queues. SIAM J. Comput., 28:1326–1346, 1999.

    Article  MathSciNet  MATH  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  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. R. B. Dial, F. Glover, D. Karney, and D. Klingman. A Computational Analysis of Alternative Algorithms and Labeling Techniques for Finding Shortest Path Trees. Networks, 9:215–248, 1979.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. 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 

  11. L. Ford. Network Flow Theory. Technical Report P-932, The Rand Corporation, 1956.

    Google Scholar 

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

    Google Scholar 

  13. 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  MathSciNet  Google Scholar 

  14. 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  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  16. F. Glover, R. Glover, and D. Klingman. Computational Studyof an Improved Shortest Path Algorithm. Networks, 14:25–37, 1984.

    Article  Google Scholar 

  17. A. V. Goldberg. A Simple Shortest Path Algorithm with Linear Average Time. Technical Report STAR-TR-01-03, STAR Lab., InterTrust Tech., Inc., Santa Clara, CA, USA, 2001.

    Google Scholar 

  18. A. V. Goldberg and C. Silverstein. Implementations of Dijkstra’s Algorithm Based on Multi-Level Buckets. In P. M. Pardalos, D.W. Hearn, and W.W. Hages, editors, Lecture Notes in Economics and Mathematical System 450 (Refereed Proceedings), pages 292–327. Springer Verlag, 1997.

    Google Scholar 

  19. T. Hagerup. Improved Shortest Paths in the Word RAM. In 27th Int. Colloq. on Automata, Languages and Programming, Geneva, Switzerland, pages 61–72, 2000.

    Google Scholar 

  20. D. B. Johnson. Efficient Algorithms for Shortest Paths in Sparse Networs. J. Assoc. Comput. Mach., 24:1–13, 1977.

    Article  Google Scholar 

  21. U. Meyer. Single-Source Shortest Paths on Arbitrary Directed Graphs in Linear Average Time. In Proc. 12th ACM-SIAM Symposium on Discrete Algorithms, pages 797–806, 2001. A full version available as TR MPI-I-2001-1-002, Max-Planck-Institut für Informatik, Saarbrüken, Germany.

    Google Scholar 

  22. B. M. E. Moret and H. D. Shapiro. An Empirical Analysis of Algorithms for Constructing a Minimum Spanning Tree. In Proc. 2nd Workshop on Algorithms and Data Structures, 1991.

    Google Scholar 

  23. K. Noshita. A Theorem on the Expected Complexityof Dijkstra’s Shortest Path Algorithm. J. Algorithms, 6:400–408, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Raman. Fast Algorithms for Shortest Paths and Sorting. Technical Report TR 96-06, King’s Colledge, London, 1996.

    Google Scholar 

  25. R. Raman. PriorityQue ues: Small, Monotone and Trans-Dichotomous. In Proc. 4th Annual European Symposium Algorithms, pages 121–137. Springer-Verlag, Lect. Notes in CS 1136, 1996.

    Google Scholar 

  26. R. Raman. Recent Results on Single-Source Shortest Paths Problem. SIGACT News, 28:81–87, 1997.

    Article  Google Scholar 

  27. R. E. Tarjan. Data Structures and Network Algorithms. Societyf or Industrial and Applied Mathematics, Philadelphia, PA, 1983.

    Google Scholar 

  28. M. Thorup. Undirected Single-Source Shortest Paths with Positive IntegerWeights in Linear Time. J. Assoc. Comput. Mach., 46:362–394, 1999.

    Article  MATH  Google Scholar 

  29. M. Thorup. On RAM Priority Queues. SIAM Journal on Computing, 30:86–109, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  30. J. W. J. Williams. Algorithm 232 (Heapsort). Comm. ACM, 7:347–348, 1964.

    Google Scholar 

  31. F. B. Zhan and C. E. Noon. Shortest Path Algorithms: An Evaluation using Real Road Networks. Transp. Sci., 32:65–73, 1998.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goldberg, A.V. (2001). Shortest Path Algorithms: Engineering Aspects. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_43

Download citation

  • DOI: https://doi.org/10.1007/3-540-45678-3_43

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics