Hardness of Preemptive Finite Capacity Dial-a-Ride
نویسنده
چکیده
In the Finite Capacity Dial-a-Ride problem the input is a metric space, a set of objects {di}, each specifying a source si and a destination ti, 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(log N), O(k)}-approximation algorithm for the preemptive version of the problem. In this paper we show that the preemptive Finite Capacity Dial-a-Ride problem has no min{O(log N), k}-approximation algorithm for any ε > 0 unless all problems in NP can be solved by randomized algorithms with expected running time O(n).
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تاریخ انتشار 2006