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Computing the n × m Shortest Paths Efficiently

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Algorithm Engineering and Experimentation (ALENEX 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1619))

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Abstract

Computation of all the shortest paths between multiple sources and multiple destinations on various networks is required in many problems, such as the traveling salesperson problem (TSP) and the vehicle routing problem (VRP). This paper proposes new algorithms that compute the set of shortest paths efficiently by using the A* algorithm. The efficiency and properties of these algorithms are examined by using the results of experiments on an actual road network.

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References

  1. A. Barr and E. A. Feigenbaum, Handbook of Artificial Intelligence, William Kaufman, Inc., Los Altos, Calif., 1981.

    MATH  Google Scholar 

  2. J. L. Bentley, “Multidimensional Binary Search Trees Used for Associative Searching,” Commun. ACM, vol. 18, no. 9, 1975, pp. 509–517.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. Champeaus, “Bidirectional Heuristic Search Again,” J. ACM, vol. 30, 1983, pp.22–32.

    Article  Google Scholar 

  4. B. V. Cherkassky, A. V. Goldberg, and C. Silverstein, “Buckets, heaps, lists and monotone priority queues,” Proc. 8th ACM-SIAM Symposium on Discrete Algorithms, 1997, pp. 83–92.

    Google Scholar 

  5. R. Dechter and J. Pearl, “Generalized Best-First Search Strategies and the Optimality of A*,” J. ACM, vol. 32, no. 3, 1985, pp. 505–536.

    Article  MATH  MathSciNet  Google Scholar 

  6. E. Dijkstra, “A Note on Two Problems in Connection with Graphs,” Numerical Mathematics, vol. 1, 1959, pp. 395–412.

    Article  MathSciNet  Google Scholar 

  7. M. L. Fredman and R. E. Tarjan, “Fibonacci Heaps and Their Uses in Improved Network Optimization Algorithms,” J. ACM, vol. 34, no. 3, 1987, pp. 596–615.

    Article  MathSciNet  Google Scholar 

  8. M. L. Fredman and D. E. Willard, “Trans-dichotomous algorithms for minimum spanning trees and shortest paths,” J. Comp. Syst. Sc. vol. 48, 1994, pp. 533–551.

    Article  MATH  MathSciNet  Google Scholar 

  9. D. Gelperin, “On the Optimality of A*,” Artif. Intell. vol. 8, no. 1, 1977, pp. 69–76.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. E. Hart, N. J. Nillson, and B. Rafael, “A Formal Basis for the Heuristic Determination of Minimum Cost Paths,” IEEE Trans. Sys. Sci. and Cyb. SSC-4, 1968, pp. 100–107.

    Google Scholar 

  11. T. Hiraga, Y. Koseki, Y. Kajitani, and A. Takahashi, “An Improved Bidirectional Search Algorithm for the 2 Terminal Shortest Path,” The 6th Karuizawa Workshop on Circuits and Systems, 1993, pp. 249–254 (in Japanese).

    Google Scholar 

  12. T. Ikeda, M. Y. Hsu, H. Imai, S. Nishimura, H. Shimoura, K. Tenmoku, and K. Mitoh, “A Fast Algorithm For Finding Better Routes By AI Search Techniques,” IEEE VNIS’94, 1994, pp. 90–99.

    Google Scholar 

  13. M. Luby and P. Ragde, “A Bidirectional Shortest-Path Algorithm With Good Average-Case Behavior,” Proc. 12th International Colloquium on Automata, Languages and Programming, LNCS 194, 1985, pp. 394–403.

    Chapter  Google Scholar 

  14. N. J. Nilsson, Problem-Solving Methods in Artificial Intelligence, McGraw-Hill, New York, 1971.

    Google Scholar 

  15. N. J. Nilsson, Principles of Artificial Intelligence, Tioga, Palo Alto, Calif., 1980.

    MATH  Google Scholar 

  16. I. Pohl, “Bi-Directional Search,” Machine Intelligence, vol. 6, pp. 127–140, 1971.

    MATH  Google Scholar 

  17. R. Raman, “Priority queues: small monotone, and trans-dichotomous,” Proc. ESA’96, LNCS 1136, 1996, pp. 121–137.

    Google Scholar 

  18. R. Raman, “A summary of shortest path results,” Technical Report TR 96-13, Kings College, London, 1996.

    Google Scholar 

  19. Y. Shirai and J. Tsuji, “Artificial Intelligence,” Iwanami Course: Information Science, vol. 22, Iwanami, Japan, 1982 (in Japanese).

    Google Scholar 

  20. M. Thorup, “On RAM priority queues,” Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 59–67.

    Google Scholar 

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Author information

Authors and Affiliations

  1. IBM Research Division, Tokyo Research Laboratory, 1623-14, Shimotsuruma, Yamato-shi, Kanagawa, 242-8502, Japan

    Tetsuo Shibuya

Authors
  1. Tetsuo Shibuya
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Editor information

Editors and Affiliations

  1. Department of Computer Science, John Hopkins University, Baltimore, MD, 21218, USA

    Michael T. Goodrich

  2. Department of Mathematics and Computer Science, Amherst University, Amherst, MA, 01002, USA

    Catherine C. McGeoch

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© 1999 Springer-Verlag Berlin Heidelberg

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Shibuya, T. (1999). Computing the n × m Shortest Paths Efficiently. In: Goodrich, M.T., McGeoch, C.C. (eds) Algorithm Engineering and Experimentation. ALENEX 1999. Lecture Notes in Computer Science, vol 1619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48518-X_13

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  • DOI: https://doi.org/10.1007/3-540-48518-X_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66227-3

  • Online ISBN: 978-3-540-48518-6

  • eBook Packages: Springer Book Archive

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