The Traveling Salesman Problem (TSP) is a central topic in discrete mathematics and theoretical computer science. It has been one of the driving forces in combinatorial optimization. The design and analysis of better and better approximation algorithms for the TSP has proved challenging but very fruitful. This is the first book on approximation algorithms for the TSP, featuring a comprehensive collection of all major results and an overview of the most intriguing open problems. Many of the presented results have been discovered only recently, and some are published here for the first time, including better approximation algorithms for the asymmetric TSP and its path version. This book constitutes and advances the state of the art and makes it accessible to a wider audience. Featuring detailed proofs, over 170 exercises, and 100 color figures, this book is an excellent resource for teaching, self-study, and further research.

About the Authors

Vera Traub has been Professor at the University of Bonn since 2023. Her research has received multiple awards, particularly her work on approximation algorithms for network design and the traveling salesman problem, including in 2023 the Maryam Mirzakhani New Frontiers Prize and the Heinz Maier-Leibnitz Prize. She is a member of the Hausdorff Center for Mathematics.

Jens Vygen has been Professor at the University of Bonn since 2003. His work comprises many aspects of combinatorial optimization and its applications, notably to chip design and vehicle routing. He has co-authored two textbooks, organized several workshops and conferences, and has been co-editor of several scientific journals and books. He is a member of the Hausdorff Center for Mathematics.

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