Advertisement

Non-additive Shortest Paths

  • George Tsaggouris
  • Christos Zaroliagis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3221)

Abstract

The non-additive shortest path (NASP) problem asks for finding an optimal path that minimizes a certain multi-attribute non-linear cost function. In this paper, we consider the case of a non-linear convex and non-decreasing function on two attributes. We present an efficient polynomial algorithm for solving a Lagrangian relaxation of NASP. We also present an exact algorithm that is based on new heuristics we introduce here, and conduct a comparative experimental study with synthetic and real-world data that demonstrates the quality of our approach.

Keywords

Short Path Optimal Path Exact Algorithm Lagrangian Relaxation Short Path Problem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ahuja, R., Magnanti, T., Orlin, J.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)Google Scholar
  2. 2.
    Beasley, J., Christofides, N.: An Algorithm for the Resource Constrained Shortest Path Problem. Networks 19, 379–394 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cheney, E.W.: Introduction to Approximation Theory. McGraw-Hill, New York (1966)zbMATHGoogle Scholar
  4. 4.
    Gabriel, S., Bernstein, D.: The Traffic Equilibrium Problem with Nonadditive Path Costs. Transportation Science 31(4), 337–348 (1997)zbMATHCrossRefGoogle Scholar
  5. 5.
    Gabriel, S., Bernstein, D.: Nonadditive Shortest Paths: Subproblems in Multi- Agent Competitive Network Models. Comp. & Math. Organiz. Theory 6 (2000)Google Scholar
  6. 6.
    Handler, G., Zang, I.: A Dual Algorithm for the Constrained Shortest Path Problem. Networks 10, 293–310 (1980)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Henig, M.: The Shortest Path Problem with Two Objective Functions. European Journal of Operational Research 25, 281–291 (1985)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Hensen, D., Truong, T.: Valuation of Travel Times Savings. Journal of Transport Economics and Policy, 237–260 (1985)Google Scholar
  9. 9.
    Mehlhorn, K., Ziegelmann, M.: Resource Constrained Shortest Paths. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 326–337. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Mirchandani, P., Wiecek, M.: Routing with Nonlinear Multiattribute Cost Functions. Applied Mathematics and Computation 54, 215–239 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Papadimitriou, C., Yannakakis, M.: On the Approximability of Trade-offs and Optimal Access of Web Sources. In: Proc. 41st FOCS 2000, pp. 86–92 (2000)Google Scholar
  12. 12.
    Scott, K., Bernstein, D.: Solving a Best Path Problem when the Value of Time Function is Nonlinear, preprint 980976 of the Transport. Research Board (1997)Google Scholar
  13. 13.
    Tsaggouris, G., Zaroliagis, C.: Non-Additive Shortest Paths, Tech. Report TR-2004/03/01, Computer Technology Institute, Patras (March 2004)Google Scholar
  14. 14.
    Zhan, F.B., Noon, C.E.: Shortest Path Algorithms: An Evaluation using Real Road Networks. Transportation Science 32(1), 65–73 (1998)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • George Tsaggouris
    • 1
    • 2
  • Christos Zaroliagis
    • 1
    • 2
  1. 1.Computer Technology InstitutePatrasGreece
  2. 2.Department of Computer Engineering and InformaticsUniversity of PatrasPatrasGreece

Personalised recommendations