An Improved Approximation Algorithm for the Capacitated Arc Routing Problem

2025-08-07

AI Summary

This paper studies the Capacitated Arc Routing Problem (CARP) under unit-demand constraints, aiming to improve the long-standing approximation ratio bound. Inspired by recent advances in the Capacitated Vehicle Routing Problem (CVRP), we propose a combinatorial optimization algorithm that integrates graph decomposition with path reconstruction: first performing a fine-grained structural decomposition of the demand graph, then constructing feasible solutions via enhanced Eulerian augmentation and matching techniques. Our algorithm achieves the first theoretical improvement in thirty years, raising the CARP approximation ratio from Jansen’s (1993) $5/2 - 1.5/k$ to $5/2 - Theta(1/sqrt{k})$. This result not only substantially outperforms all prior bounds but also establishes a systematic connection between approximation techniques for CARP and CVRP, providing a novel framework for future research.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Other Foundations of Planning, Routing & Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 $(frac{5}{2}-Θ(frac{1}{sqrt{k}}))$-approximation algorithm, which to the best of our knowledge constitutes the first improvement over Jansen's bound.

Problem

• Improving approximation for Capacitated Arc Routing Problem
• Enhancing Jansen's 1993 algorithm performance ratio
• First advancement beyond $frac{5}{2}-frac{1.5}{k}$ approximation bound

Innovation

• Improved approximation algorithm for CARP
• Better ratio than Jansen's bound
• First advancement since 1993