Hardness of Preemptive Finite Capacity Dial-a-Ride

  • Inge Li Gørtz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4110)


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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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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