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: 5, Informative) by bradley13 on Tuesday October 10 2017, @08:22AM (2 children)
I didn't read TFA, because this is Soylent. However, from TFS:
"We give a constant-factor approximation algorithm..." The word "approximation" means that there is no guarantee of an optimal solution. There are lots of algorithms for getting "pretty good" solutions, or even optimal solutions "most of the time" for NP-complete problems in polynomial time. So: this result presumably offers nothing new, except maybe a different way of doing the approximation.
Everyone is somebody else's weirdo.
(Score: 2) by TheRaven on Tuesday October 10 2017, @10:38AM (1 child)
sudo mod me up
(Score: 0) by Anonymous Coward on Thursday October 12 2017, @07:07PM
> the travelling salesman problem is much easier to solve if you place some constraints
Goodness me yes! It's an absolutely tractable problem under lots of conditions. I forget what boundaries are big-O (complexity) better and which are just empirically useful, but some which have been investigated include: directed graphs, trees, planar graphs, maximum degree (# of edges/node), bounded edge length...
There's some pretty amazing properties where, like including or excluding '0' from the domain of a function, suddenly the problem can have a vastly different meaning.
Any graph maths or CS types around here able to link to an understandable overview of modified travelling salesman?