Computational geometry: an introduction
Computational geometry: an introduction
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
The vehicle routing problem
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A quasi-polynomial time approximation scheme for Euclidean capacitated vehicle routing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The train delivery problem: vehicle routing meets bin packing
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
The school bus problem on trees
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
| Hi-index | 0.00 |
Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P.The k-tour cover problem is known to be $\mathcal{NP}$-hard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomial-time approximation scheme (PTAS) for small values of k, $k=\O(\log n / \log\log n)$.In this paper, we significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of $k \le 2^{\log^{\delta}n}$, where 驴 = 驴(驴). The main technical result proved in the paper is a novel reduction of the k-tour cover problem with a set of n points to a small set of instances of the problem, each with $\O((k/\epsilon)^{\O(1)})$ points.