# A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem

@article{vanBevern2020AHN, title={A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem}, author={Ren{\'e} van Bevern and Viktoriia A. Slugina}, journal={ArXiv}, year={2020}, volume={abs/2004.02437} }

## 14 Citations

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…

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.

Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

- Computer Science, MedicineFrontiers in Robotics and AI
- 2021

A new approach for two-dimensional symmetric problems with more than a million coordinates is proposed that is able to create good initial tours within few minutes and is superior to state-of-the-art methods when applied to TSP instances with non-uniformly distributed coordinates.

A (slightly) improved approximation algorithm for metric TSP

- Computer Science, MathematicsSTOC
- 2021

For some > 10−36 the authors give a randomized 3/2− approximation algorithm for metric TSP, which is equivalent to a randomized 2/3− approximation for standard TSP.

Approximation Algorithms for Multi-vehicle Stacker Crane Problems

- Journal of the Operations Research Society of China
- 2022

Approximating TSP walks in subcubic graphs

- Computer Science, MathematicsArXiv
- 2021

We prove that every simple 2-connected subcubic graph on n vertices with n2 vertices of degree 2 has a TSP walk of length at most 5n+n2 4 − 1, confirming a conjecture of Dvořák, Král’, and Mohar.…

Approximation algorithms for some min-max postmen cover problems

- Computer ScienceAnn. Oper. Res.
- 2021

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.

Recent Advances in Scheduling Theory and Applications in Robotics and Communications

- Computer ScienceDCCN
- 2021

Reinforcement Learning for Combinatorial Optimization: A Survey

- Computer Science, MathematicsComput. Oper. Res.
- 2021

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