Book contents
- Frontmatter
- 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
9 - Asymmetric Path TSP
Published online by Cambridge University Press: 14 November 2024
Book contents
- Frontmatter
- 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
Summary
A natural generalization of the (asymmetric) traveling salesman problem arises when we are given a start vertex s and an end vertex t and ask for a tour that begins in s and ends in t, rather than a round trip.
While this problem seems to be harder, we will see in this chapter that it can be tackled by similar techniques. In particular, we show black-box reductions (by Feige and Singh, and by Köhne, Traub, and Vygen) to Asymmetric TSP and prove, as new results, the best-known approximation ratios and bounds on the integrality ratio of the natural LP relaxation.
- Type
- Chapter
- Information
- Approximation Algorithms for Traveling Salesman Problems , pp. 183 - 211Publisher: Cambridge University PressPrint publication year: 2024