A New Dual Algorithm for Shortest Path Reoptimization

  • Sang Nguyen
  • Stefano Pallottino
  • Maria Grazia Scutellà
Part of the Applied Optimization book series (APOP, volume 63)


Shortest path problems are among the most studied network flow problems, with interesting applications in various fields. In large scale transportation systems, a sequence of shortest path problems must often be solved, where the (k + 1) st problem differs only slightly from the k th one. Significant reduction in computational time may be obtained from an efficient reoptimization procedure that exploits the useful information available after each shortest path computation in the sequence. Such reduction in computational time is essential in many on-line applications. This work is devoted to the development of such reoptimization algorithm. We shall focus on the sequence of shortest path problems to be solved for which problems differ by the origin node of the path set. After reviewing the classical algorithms described in the literature so far, which essentially show a Dijkstra-like behavior, a new dual approach will be proposed, which could be particularly promising in practice.


Short Path Short Path Problem Close Node Short Path Tree Dual Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Ahuja, R. K., Magnanti, T. L. and Orlin, J. B. (1993). Network flows: Theory, algorithms, and applications. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  2. Bertsekas, D. P., Pallottino, S. and Scutellà, M. G. (1995). “Polynomial Auction algorithms for shortest paths”. Computational Optimization and Applications 4, 99–125.CrossRefGoogle Scholar
  3. Dijkstra, E. W. (1959). “A note on two problems in connexion with graphs”. Numerische Mathematik 1, 269–271.CrossRefGoogle Scholar
  4. Dionne, R. (1978). “Etude et extension d’un algorithme de Murchland”. INFOR 16, 132–146.Google Scholar
  5. Florian, M., Nguyen, S. and Pallottino, S. (1981). “A dual simplex algorithm for finding all shortest paths” Networks 11, 367–378.CrossRefGoogle Scholar
  6. Fujishige, S. (1981). “A note on the problem of updating shortest paths”. Networks 11, 317–319.CrossRefGoogle Scholar
  7. Gallo, G. (1980). “Reoptimization procedures in shortest path problems”. Rivista di Matematica per le Scienze Economiche e Sociali 3, 3–13.CrossRefGoogle Scholar
  8. Gallo, G. and Pallottino, S. (1982). “A new algorithm to find the shortest paths between all pairs of nodes”. Discrete Applied Mathematics 4, 23–35.CrossRefGoogle Scholar
  9. Lawler, E. L. (1976). Combinatorial optimization: Networks and matroids. Holt, Rinehart and Winston, New York.Google Scholar
  10. Murchland, J. D. (1970). A fixed matrix method for all shortest distances in a directed graph and for the inverse problem. Ph.D. Thesis, Univ. of Karlsruhe.Google Scholar
  11. Nemhauser, G. (1972). “A generalized permanent label setting algorithm for the shortest path between specified nodes”. Journal of Mathematical Analysis and Applications 38, 328–334.CrossRefGoogle Scholar
  12. Pallottino, S. and Scutellà, M. G. (1997). “Dual algorithms for the shortest path tree problem”. Networks 29, 125–133.CrossRefGoogle Scholar
  13. Pallottino, S. and Scutellà, M. G. (1998). “Shortest path algorithms in transportation models: classical and innovative aspects”. in ( Marcotte, P. and Nguyen, S., Eds.) Equilibrium and advanced transportation modelling, Kluwer, Boston, 245–281.CrossRefGoogle Scholar
  14. Tarjan, R. E. (1983). Data structures and network algorithms. SIAM, Philadelphia, PA.CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Sang Nguyen
  • Stefano Pallottino
  • Maria Grazia Scutellà

There are no affiliations available

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