The Finite Capacity Dial-A-Ride Problem

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(log1/4N), k1}-approximation algorithm for any > 0 unless all problems in NP can be solved by randomized algorithms with expected running time O(npolylogn ).

• Type: Conference
• Year: 1998
• Where: FOCS
• Authors: Moses Charikar, Balaji Raghavachari
• Keywords: Capacity Dial-a-Ride Problem, Finite Capacity Dial-a-Ride, FOCS 1998, Preemptive Version, Theoretical Computer Science