Approximation Algorithms for Traveling Salesman Problems

Vera Traub, Jens Vygen

• Publisher: Cambridge University Press
• Year: 2024
• eBook ISBN: 9781009445429
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title
• Endorsements
• Title page
• Imprints page
• Preface
• Contents
• 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