In the Finite Capacity Dial-a-Ride problem the input is a metric space, a set of objects {d i }, each specifying a source s i and a destination t i , and an integer k—the capacity of the vehicle used for making the deliveries. The goal is to compute a shortest tour for the vehicle in which all objects can be delivered from their sources to their destinations while ensuring that the vehicle carries at most k objects at any point in time. In the preemptive version an object may be dropped at intermediate locations and picked up later and delivered. Let N be the number of nodes in the input graph. Charikar and Raghavachari [FOCS ’98] gave a min {O(logN),O(k)}-approximation algorithm for the preemptive version of the problem. In this paper has no min {O(log\(^{\rm 1/4-{\it \epsilon}}\) N),k 1 − ε}-approximation algorithm for any ε> 0 unless all problems in NP can be solved by randomized algorithms with expected running time O(n polylog n ).


Approximation Algorithm Source Node Travel Salesman Problem Travel Salesman Problem Random String 
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  1. 1.
    Andrews, M.: Hardness of buy-at-bulk network design. In: 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 115–124 (October 2004)Google Scholar
  2. 2.
    Andrews, M., Zhang, L.: Bounds on fiber minimization in optical networks with fixed fiber capacity. In: IEEE INFOCOM (2005)Google Scholar
  3. 3.
    Charikar, M., Khuller, S., Raghavachari, B.: Algorithms for capacitated vehicle routing. SICOMP: SIAM Journal on Computing 31(3), 665–682 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Charikar, M., Raghavachari, B.: The finite capacity dial-a-ride problem. In: IEEE Symposium on Foundations of Computer Science, pp. 458–467 (1998)Google Scholar
  5. 5.
    Christofedes, N.: Vehicle routing. In: Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B. (eds.) The Traveling Salesman Problem, pp. 431–448. John Wiley, Chichester (1985)Google Scholar
  6. 6.
    Desaulniers, G., Desrosiers, J., Erdmann, A., Solomon, M.M., Soumis, F.: VRP with pickup and delivery. In: Toth, P., Vigo, D. (eds.) The vehicle routing problem, pp. 225–242. Society for Industrial and Applied Mathematics (2001)Google Scholar
  7. 7.
    Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. J. Comput. System Sci. 69(3), 385–497 (2004)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Frederickson, G.N., Guan, D.J.: Non-preemptive ensemble motion planning on a tree. Journal of Algorithms 15(1), 29–60 (1993)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Frederickson, G.N., Hecht, M.S., Kim, C.E.: Approximation algorithms for some routing problems. SIAM Journal on Computing 7(2), 178–193 (1978)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Golden, B.L., Assad, A.A.: Vehicle Routing: Methods and Studies. Studies in Management Science and Systems, vol. 16. Elsevier, Amsterdam (1991)Google Scholar
  11. 11.
    Gørtz, I.L.: Hardness of preemptive finite capacity dial-a-ride. IMADA Preprints 2006 No. 4, University of Southern Denmark (2006)Google Scholar
  12. 12.
    Guan, D.J.: Routing a vehicle of capacity greater than one. Discrete Applied Mathematics 81(1-3) (1998)Google Scholar
  13. 13.
    Haimovich, M., Kan, A.H.G.R.: Bounds and heuristics for capacitated routing problems. Mathematics of Operations Research 10(4), 527–542 (1985)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Psaraftis, H.N.: An exact algorithm for the single vehicle many-to-many dial-a-ride problem with time windows. Transportation Science 17(3), 351–357 (1983)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Inge Li Gørtz
    • 1
  1. 1.Technical University of Denmark 

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