Better approximation guarantee for Asymmetric TSP

2026-03-15

AI Summary

This study addresses the asymmetric traveling salesman problem (ATSP) on directed graphs and its variants—including minimum-cost tours in unweighted digraphs and tours with specified endpoints—with the aim of overcoming performance bottlenecks in existing approximation algorithms. By integrating linear programming relaxations, combinatorial optimization, and graph-theoretic techniques, the work introduces a novel algorithmic framework and refined analytical methods. The main contributions include the first approximation ratio for ATSP below 15, improved theoretical guarantees for several problem variants, and tighter upper bounds on the integrality gap of the standard LP relaxation.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

Abstract

We improve the approximation ratio for the Asymmetric TSP to less than 15. We also obtain improved ratios for the special case of unweighted digraphs and the generalization where we ask for a minimum-cost tour with given (distinct) endpoints. Moreover, we prove better upper bounds on the integrality ratios of the natural LP relaxations.

Problem

• Asymmetric TSP
• approximation ratio
• integrality ratio
• unweighted digraphs
• minimum-cost tour

Innovation

• Asymmetric TSP
• approximation ratio
• integrality ratio
• LP relaxation
• unweighted digraphs