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from the problem-of-looking-for-an-asymmetric-traveling-salesman dept.
The real-world version of the famous traveling salesman problem finally gets a good-enough solution.
From the abstract on arXiv https://arxiv.org/abs/1708.04215 (full article is available):
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 arising from node-weighted metrics. For those instances, we then solve Local-Connectivity ATSP, a problem known to be equivalent (in terms of constant-factor approximation) to the asymmetric traveling salesman problem.
[1] LP == Linear Programming
[2] ATSP == Asymmetric Traveling Salesman Problem
Any Soylentils able to explain what, if any, impact this research has on the class of NP-complete problems?
source:
https://www.quantamagazine.org/one-way-salesman-finds-fast-path-home-20171005/
(Score: 1, Touché) by Anonymous Coward on Tuesday October 10 2017, @12:02PM (2 children)
But, how many pubs do you stop at on the way home? And do you visit them in an optimal sequence??
(Score: 2) by turgid on Tuesday October 10 2017, @07:06PM
I'm not a One-Way Salesman.
I refuse to engage in a battle of wits with an unarmed opponent [wikipedia.org].
(Score: 2) by bob_super on Tuesday October 10 2017, @09:49PM
Is the "optimal sequence" really based on distance? I thought it was based on high-to-low attractiveness of female patrons, which solves the order-of-visit question and therefore nullifies the TSP altogether.