# An improved approximation algorithm for ATSP

@article{Traub2020AnIA, title={An improved approximation algorithm for ATSP}, author={Vera Traub and Jens Vygen}, journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing}, year={2020} }

We revisit the constant-factor approximation algorithm for the asymmetric traveling salesman problem by Svensson, Tarnawski, and Végh [STOC 2018]. We improve on each part of this algorithm. We avoid the reduction to irreducible instances and thus obtain a simpler and much better reduction to vertebrate pairs. We also show that a slight variant of their algorithm for vertebrate pairs has a much smaller approximation ratio. Overall we improve the approximation ratio from 506 to 22+ε for any ε > 0…

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## 11 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.

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

- Computer Science, MathematicsSTOC
- 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…

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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.

A 2-Approximation Algorithm for the Complementary Maximal Strip Recovery Problem

- Mathematics, Computer ScienceCPM
- 2019

A new approximation algorithm for the Complementary Maximal Strip Recovery (CMSR) problem is presented, improving the currently best 7/3-approximation algorithm.

A 3/2-Approximation for the Metric Many-visits Path TSP

- Mathematics, Computer ScienceArXiv
- 2020

A polynomial-time algorithm to compute a connected, degree bounded multigraph of minimum cost and a $\frac32$-approximation for the problem of scheduling classes of jobs with sequence-dependent setup times on a single machine so as to minimize the makespan.

Approximation Algorithms for the Single Robot Line Coverage Problem

- Computer ScienceWAFR
- 2021

This work considers here the line coverage problem for a single robot where the service and deadhead costs are treated separately, and are asymmetric, and presents approximation algorithms to obtain bounded solutions efficiently, using the minimum cost flow problem.

A constant-factor approximation for directed latency in quasi-polynomial time

- Journal of Computer and System Sciences
- 2021

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.

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.

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