# A constant-factor approximation algorithm for the asymmetric traveling salesman problem

@article{Svensson2018ACA, title={A constant-factor approximation algorithm for the asymmetric traveling salesman problem}, author={Ola Svensson and Jakub Tarnawski and L{\'a}szl{\'o} A. V{\'e}gh}, journal={Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing}, year={2018} }

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation. Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics. Specifically, we give a generic reduction to structured instances that resemble but are more general than those…

## 42 Citations

A Constant-factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem

- Mathematics, Computer ScienceJ. ACM
- 2020

A constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP) is given, showing that any algorithm for Subtour Partition Cover can be turned into an algorithm for ATSP while only losing a small constant factor in the performance guarantee.

Ju n 20 19 A Constant-Factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem *

- 2019

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus…

Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem

- Computer ScienceACM Trans. Algorithms
- 2021

It is shown how the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi.

Beating the Integrality Ratio for s-t-Tours in Graphs

- Mathematics, Computer Science2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
- 2018

This paper devise a polynomial-time algorithm for the s-t-path graph TSP with approximation ratio 1.497 and introduces several completely new techniques, including a new type of ear-decomposition, an enhanced ear induction that reveals a novel connection to matroid union, a stronger lower bound, and a reduction of general instances to instances in which s and t have small distance.

Fast Approximation Algorithms for Bounded Degree and Crossing Spanning Tree Problems

- Mathematics, Computer ScienceAPPROX-RANDOM
- 2021

A fast near-linear time implementation of swap-rounding in the spanning tree polytope of a graph and a fractional solution that can be used to sparsify the input graph and lead to significantly faster approximation algorithms than known before.

A Constant-Factor Approximation for Directed Latency in Quasi-Polynomial Time

- Mathematics, Computer ScienceESA
- 2020

The first constant-factor approximation for the Directed Latency problem in quasi-polynomial time is given, and the standard Asymmetric TSP-Path integrality gap is shown to be bounded by a constant.

From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization

- Computer Science, MathematicsFCT
- 2021

The tree doubling and Christofides algorithm are generalized and a parameterized 3-approximation is derived, where the parameter is the number of asymmetric edges in a given minimum spanning arborescence, which yields algorithms to efficiently compute constant factor approximations also for moderately asymmetric TSP instances.

Quasi-Polynomial Algorithms for Submodular Tree Orienteering and Directed Network Design Problems

- Mathematics of Operations Research
- 2021

We consider the following general network design problem. The input is an asymmetric metric (V, c), root [Formula: see text], monotone submodular function [Formula: see text], and budget B. The goal…

Constant-Factor Approximation to Deadline TSP and Related Problems in (Almost) Quasi-Polytime

- Computer ScienceICALP
- 2021

This work investigates a genre of vehicle-routing problems (VRPs) wherein nodes located in a metric space have associated rewards that depend on their visiting times, and argues that the problem of finding a path between two consecutive guessed nodes can be relaxed to an instance of a special case of deadline TSP called point-to-point (P2P) orienteering.

Bipartite TSP in o(1.9999ⁿ) time, assuming quadratic time matrix multiplication

- Computer Science, MathematicsSTOC
- 2020

A fast algorithm for MinHamPair is given based on a new sparse cut-based factorization of the ‘matchings connectivity matrix’, introduced by Cygan et al.

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A constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP) is given, showing that any algorithm for Subtour Partition Cover can be turned into an algorithm for ATSP while only losing a small constant factor in the performance guarantee.

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