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Non-additive Shortest Paths

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Algorithms – ESA 2004 (ESA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3221))

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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.

This work was partially supported by the IST Programme (6th FP) of EC under contract No. IST-2002-001907 (integrated project DELIS).

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References

  1. Ahuja, R., Magnanti, T., Orlin, J.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)

    Google Scholar 

  2. Beasley, J., Christofides, N.: An Algorithm for the Resource Constrained Shortest Path Problem. Networks 19, 379–394 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cheney, E.W.: Introduction to Approximation Theory. McGraw-Hill, New York (1966)

    MATH  Google Scholar 

  4. Gabriel, S., Bernstein, D.: The Traffic Equilibrium Problem with Nonadditive Path Costs. Transportation Science 31(4), 337–348 (1997)

    Article  MATH  Google Scholar 

  5. Gabriel, S., Bernstein, D.: Nonadditive Shortest Paths: Subproblems in Multi- Agent Competitive Network Models. Comp. & Math. Organiz. Theory 6 (2000)

    Google Scholar 

  6. Handler, G., Zang, I.: A Dual Algorithm for the Constrained Shortest Path Problem. Networks 10, 293–310 (1980)

    Article  MathSciNet  Google Scholar 

  7. Henig, M.: The Shortest Path Problem with Two Objective Functions. European Journal of Operational Research 25, 281–291 (1985)

    Article  MathSciNet  Google Scholar 

  8. Hensen, D., Truong, T.: Valuation of Travel Times Savings. Journal of Transport Economics and Policy, 237–260 (1985)

    Google Scholar 

  9. Mehlhorn, K., Ziegelmann, M.: Resource Constrained Shortest Paths. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 326–337. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  10. Mirchandani, P., Wiecek, M.: Routing with Nonlinear Multiattribute Cost Functions. Applied Mathematics and Computation 54, 215–239 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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. Tsaggouris, G., Zaroliagis, C.: Non-Additive Shortest Paths, Tech. Report TR-2004/03/01, Computer Technology Institute, Patras (March 2004)

    Google Scholar 

  14. Zhan, F.B., Noon, C.E.: Shortest Path Algorithms: An Evaluation using Real Road Networks. Transportation Science 32(1), 65–73 (1998)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Technology Institute, P.O. Box 1122, 26110, Patras, Greece

    George Tsaggouris & Christos Zaroliagis

  2. Department of Computer Engineering and Informatics, University of Patras, 26500, Patras, Greece

    George Tsaggouris & Christos Zaroliagis

Authors
  1. George Tsaggouris
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  2. Christos Zaroliagis
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Editor information

Editors and Affiliations

  1. University of Freiburg, Georges Köhler Allee 79, 79110, Freiburg, Germany

    Susanne Albers

  2. Department of Computer Science, King’s College, WC2R 2LS, London, UK

    Tomasz Radzik

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© 2004 Springer-Verlag Berlin Heidelberg

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Tsaggouris, G., Zaroliagis, C. (2004). Non-additive Shortest Paths. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_72

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  • DOI: https://doi.org/10.1007/978-3-540-30140-0_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23025-0

  • Online ISBN: 978-3-540-30140-0

  • eBook Packages: Springer Book Archive

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