An Improved Approximation Algorithm for the Capacitated Arc Routing Problem

TL;DR

This paper presents a new approximation algorithm for the Capacitated Arc Routing Problem that improves the known approximation ratio by leveraging recent advances in related vehicle routing problems.

Contribution

It introduces the first improvement over the longstanding approximation ratio for CARP by adapting techniques from CVRP approximations.

Findings

Achieves a $(rac{5}{2}- ext{Theta}(1/\sqrt{k}))$-approximation ratio

First known enhancement over Jansen's 1993 bound

Demonstrates progress in approximation algorithms for arc routing problems

Abstract

The Capacitated Arc Routing Problem (CARP), introduced by Golden and Wong in 1981, is an important arc routing problem in Operations Research, which generalizes the famous Capacitated Vehicle Routing Problem (CVRP). When every customer has a unit demand, the best known approximation ratio for CARP, given by Jansen in 1993, remains $\frac{5}{2}-\frac{1.5}{k}$, where $k$ denotes the vehicle capacity. Based on recent progress in approximating CVRP, we improve this result by proposing a $(\frac{5}{2}-\Theta(\frac{1}{\sqrt{k}}))$-approximation algorithm, which to the best of our knowledge constitutes the first improvement over Jansen's bound.