A quasi-polynomial time approximation scheme for Euclidean capacitated vehicle routing

TL;DR

This paper presents a quasi-polynomial time approximation scheme for the Euclidean capacitated vehicle routing problem, improving the efficiency of near-optimal solutions in a geometric setting.

Contribution

It introduces a novel quasi-polynomial time approximation scheme specifically for Euclidean CVRP, advancing computational methods for this classic problem.

Findings

Achieves a quasi-polynomial time approximation scheme for Euclidean CVRP.

Provides near-optimal solutions with provable approximation guarantees.

Extends the theoretical understanding of geometric vehicle routing problems.

Abstract

In the capacitated vehicle routing problem, introduced by Dantzig and Ramser in 1959, we are given the locations of n customers and a depot, along with a vehicle of capacity k, and wish to find a minimum length collection of tours, each starting from the depot and visiting at most k customers, whose union covers all the customers. We give a quasi-polynomial time approximation scheme for the setting where the customers and the depot are on the plane, and distances are given by the Euclidean metric.