Approximation Algorithms for Traveling Salesman Problems

A comprehensive collection of major results and state-of-the-art research in approximation algorithms for the Traveling Salesman Problem.

Vera Traub (Author), Jens Vygen (Author)

9781009445412, Cambridge University Press

Hardback, published 5 December 2024

444 pages
23.5 x 15.9 x 2.9 cm, 0.76 kg

'This is an amazing book by world-leading experts Vera Traub and Jens Vygen. It comprehensively covers and simplifies recent developments on approximation algorithms for the traveling salesman problem. The clarity and extensive treatment of advanced algorithmic techniques make this book a must-read for anyone interested in advanced algorithmic techniques and approximation algorithms.' Ola Svensson, École Polytechnique Fédérale de Lausanne

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.

Preface
1. Introduction
2. Linear programming relaxations of the Symmetric TSP
3. Linear programming relaxations of the Asymmetric TSP
4. Duality, cuts, and uncrossing
5. Thin trees and random trees
6. Asymmetric Graph TSP
7. Constant-factor approximation for the Asymmetric TSP
8. Algorithms for subtour cover
9. Asymmetric Path TSP
10. Parity correction of random trees
11. Proving the main payment theorem for hierarchies
12. Removable pairings
13. Ear-Decompositions, matchings, and matroids
14. Symmetric Path TSP and T-tours
15. Best-of-Many Christofides and variants
16. Path TSP by dynamic programming
17. Further results, related problems
18. State of the art, open problems
Bibliography
Index.

Subject Areas: Optimization [PBU]