Vehicle routing with time windows
Operations Research
A new optimization algorithm for the vehicle routing problem with time windows
Operations Research
On the distance constrained vehicle routing problem
Operations Research
Resource-constrained geometric network optimization
Proceedings of the fourteenth annual symposium on Computational geometry
Randomized metarounding (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Approximation Algorithms for Orienteering and Discounted-Reward TSP
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for deadline-TSP and vehicle routing with time-windows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for some vehicle routing problems
Discrete Applied Mathematics
Approximations for minimum and min-max vehicle routing problems
Journal of Algorithms
Approximation to the minimum rooted star cover problem
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
To fill or not to fill: the gas station problem
ESA'07 Proceedings of the 15th annual European conference on Algorithms
To fill or not to fill: The gas station problem
ACM Transactions on Algorithms (TALG)
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In this paper, we study the following vehicle routing problem: given n vertices in a metric space, a specified root vertex r (the depot), and a length bound D, find a minimum cardinality set of r-paths that covers all vertices, such that each path has length at most D. This problem is $\mathcal{NP}$-complete, even when the underlying metric is induced by a weighted star. We present a 4-approximation for this problem on tree metrics. On general metrics, we obtain an O(logD) approximation algorithm, and also an $(O(\log \frac{1}{\epsilon}),1+\epsilon)$ bicriteria approximation. All these algorithms have running times that are almost linear in the input size. On instances that have an optimal solution with one r-path, we show how to obtain in polynomial time, a solution using at most 14 r-paths. We also consider a linear relaxation for this problem that can be solved approximately using techniques of Carr & Vempala [7]. We obtain upper bounds on the integrality gap of this relaxation both in tree metrics and in general.