Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-linear Objectives with Applications

  • George Tsaggouris
  • Christos Zaroliagis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


We provide an improved FPTAS for multiobjective shortest paths, a fundamental (NP-hard) problem in multiobjective optimization, along with a new generic method for obtaining FPTAS to any multiobjective optimization problem with non-linear objectives. We show how these results can be used to obtain better approximate solutions to three related problems that have important applications in QoS routing and in traffic optimization.


Multiobjective Optimization Short Path Problem Multiobjective Optimization Problem Cost Vector Fully Polynomial Time Approximation Scheme 
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  1. 1.
    Ackermann, H., Newman, A., Röglin, H., Vöcking, B.: Decision Making Based on Approximate and Smoothed Pareto Curves. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 675–684. Springer, Heidelberg (2005); (full version as Tech. Report AIB-2005-23, RWTH Aachen, December 2005) CrossRefGoogle Scholar
  2. 2.
    Corley, H., Moon, I.: Shortest Paths in Networks with Vector Weights. Journal of Optimization Theory and Applications 46(1), 79–86 (1985)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ehrgott, M.: Multicriteria Optimization. Springer, Heidelberg (2000)MATHGoogle Scholar
  4. 4.
    Ehrgott, M., Gandibleux, X. (eds.): Multiple Criteria Optimization – state of the art annotated bibliographic surveys. Kluwer Academic Publishers, Boston (2002)MATHGoogle Scholar
  5. 5.
    Gabriel, S., Bernstein, D.: The Traffic Equilibrium Problem with Nonadditive Path Costs. Transportation Science 31(4), 337–348 (1997)MATHCrossRefGoogle Scholar
  6. 6.
    Gabriel, S., Bernstein, D.: Nonadditive Shortest Paths: Subproblems in Multi-Agent Competitive Network Models. Computational & Mathematical Organization Theory 6, 29–45 (2000)CrossRefGoogle Scholar
  7. 7.
    Goel, A., Ramakrishnan, K.G., Kataria, D., Logothetis, D.: Efficient Computation of Delay-Sensitive Routes from One Source to All Destinations. In: Proc. IEEE Conf. Comput. Commun. – INFOCOM (2001)Google Scholar
  8. 8.
    Hansen, P.: Bicriterion Path Problems. In: Proc. 3rd Conf. Multiple Criteria Decision Making – Theory and Applications. LNEMS, vol. 117, pp. 109–127. Springer, Heidelberg (1979)Google Scholar
  9. 9.
    Lorenz, D.H., Raz, D.: A simple efficient approximation scheme for the restricted shortest path problem. Operations Res. Lett. 28, 213–219 (2001)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Van Mieghem, P., Kuipers, F.A., Korkmaz, T., Krunz, M., Curado, M., Monteiro, E., Masip-Bruin, X., Sole-Pareta, J., Sanchez-Lopez, S.: Quality of Service Routing, ch. 3. In: Smirnov, M. (ed.) Quality of Future Internet Services. LNCS, vol. 2856, pp. 80–117. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Papadimitriou, C., Yannakakis, M.: On the Approximability of Trade-offs and Optimal Access of Web Sources. In: Proc. 41st Symp. on Foundations of Computer Science – FOCS 2000, pp. 86–92 (2000)Google Scholar
  12. 12.
    Tsaggouris, G., Zaroliagis, C.: Improved FPTAS for Multiobjective Shortest Paths with Applications, CTI Techn. Report TR-2005/07/03 (July 2005)Google Scholar
  13. 13.
    Tsaggouris, G., Zaroliagis, C.: Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-linear Objectives with Applications, CTI Techn. Report TR-2006/03/01 (March 2006)Google Scholar
  14. 14.
    Vassilvitskii, S., Yannakakis, M.: Efficiently Computing Succinct Trade-off Curves. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1201–1213. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Warburton, A.: Approximation of Pareto Optima in Multiple-Objective Shortest Path Problems. Operations Research 35, 70–79 (1987)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • George Tsaggouris
    • 1
  • Christos Zaroliagis
    • 2
  1. 1.Computer Technology InstitutePatras University CampusPatrasGreece
  2. 2.Dept of Computer Eng & InformaticsUniversity of PatrasPatrasGreece

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