A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs
Data Structures and Algorithms
2019-01-23 v1
Abstract
The Capacitated Vehicle Routing problem is to find a minimum-cost set of tours that collectively cover clients in a graph, such that each tour starts and ends at a specified depot and is subject to a capacity bound on the number of clients it can serve. In this paper, we present a polynomial-time approximation scheme (PTAS) for instances in which the input graph is planar and the capacity is bounded. Previously, only a quasipolynomial-time approximation scheme was known for these instances. To obtain this result, we show how to embed planar graphs into bounded-treewidth graphs while preserving, in expectation, the client-to-client distances up to a small additive error proportional to client distances to the depot.
Cite
@article{arxiv.1901.07032,
title = {A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs},
author = {Amariah Becker and Philip N. Klein and Aaron Schild},
journal= {arXiv preprint arXiv:1901.07032},
year = {2019}
}