On-line single-server dial-a-ride problems
Theoretical Computer Science
Online Dial-a-Ride Problems: Minimizing the Completion Time
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Cuts, Trees and -Embeddings of Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A heuristic for the Stacker Crane Problem on trees which is almost surely exact
Journal of Algorithms
Decentralized task allocation using magnet: an empirical evaluation in the logistics domain
Proceedings of the ninth international conference on Electronic commerce
Online and offline algorithms for the sorting buffers problem on the line metric
Journal of Discrete Algorithms
ACM Transactions on Algorithms (TALG)
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Selecting good a priori sequences for vehicle routing problem with stochastic demand
ICTAC'11 Proceedings of the 8th international conference on Theoretical aspects of computing
Online sorting buffers on line
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Hardness of preemptive finite capacity dial-a-ride
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We give the first non-trivial approximation algorithm for the Capacitated Dial-a-Ride problem: given a collection of objects located at points in a metric space, a specified destination point for each object, and a vehicle with a capacity of at most k objects, the goal is to compute a shortest tour for the vehicle in which all objects can be delivered to their destinations while ensuring that the vehicle carries at most k objects at any point in time. The problem is known under several names, including the Stacker Crane problem and the Dial-a-Ride problem. No theoretical approximation guarantees were known for this problem other than for the cases k=1,\infty and the trivial O(k) approximation for general capacity k. We give an algorithm with approximation ratio O(sqrt{k}) for special instances on a class of tree metrics called height-balanced trees. Using Bartal's recent results on the probabilistic approximation of metric spaces by tree metrics, we obtain an approximation ratio of O(sqrt{k} log n log log n)$ for arbitrary n point metric spaces. When the points lie on a line (line metric), we provide a 2-approximation algorithm.We also consider the Dial-a-Ride problem in another framework: when the vehicle is allowed to leave objects at intermediate locations and pick them up at a later time and deliver them. For this model, we design an approximation algorithm whose performance ratio is O(1) for tree metrics and O(log n log log n) for arbitrary metrics.We also study the ratio between the values of the optimal solutions for the two versions of the problem. We show that unlike in k-delivery TSP in which all the objects are identical, this ratio is not bounded by a constant for the Dial-a-Ride problem, and it could be as large as \Omega(k^{2/3}).