P + Optics = NP? (Apparently? Maybe? Huh?)
I’m sure that when you all got your latest issue of Optics Express you were as taken aback by An Optical Solution For The Traveling Salesman Problem as I was.
We introduce an optical method based on white light interferometry in order to solve the well-known NP–complete traveling salesman problem. To our knowledge it is the first time that a method for the reduction of non–polynomial time to quadratic time has been proposed. We will show that this achievement is limited by the number of available photons for solving the problem. It will turn out that this number of photons is proportional to NN for a traveling salesman problem with N cities and that for large numbers of cities the method in practice therefore is limited by the signal–to–noise ratio. The proposed method is meant purely as a gedankenexperiment.
So is the “Gedankenexperiment” (”thought experiment”) whether or not it can be done or whether or not people buy in to the premise of the paper? Anybody want to give a go at reading this, not glazing over, and giving an informed $0.02?
August 19th, 2007 at 6:43 pm
Apparently someone smarter than both of us came up with an explanation. It is something along the line that since you need N photons, you need N time.