Nonpreemptive ensemble motion planning on a tree
Journal of Algorithms
Routing a vehicle of capacity greater than one
Discrete Applied Mathematics
The vehicle routing problem
Algorithms for Capacitated Vehicle Routing
SIAM Journal on Computing
The Finite Capacity Dial-A-Ride Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
ESA'07 Proceedings of the 15th annual European conference on Algorithms
| Hi-index | 0.00 |
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(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),k1−ε}-approximation algorithm for any ε 0 unless all problems in NP can be solved by randomized algorithms with expected running time O(npolylog n).