Charles Stross' Diary (RSS Feed)
08-07-2007, 11:05 PM
An Optical Solution For The Traveling Salesman Problem (http://www.opticsexpress.org/abstract.cfm?id=140598)
They're claiming an O(NN) solution to a problem that is NP-complete. According to the abstract:
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.
This is either wrong, or (as Ken MacLeod put it) "we're all doomed". Anyone want to give it a read-through and tell me if it's plausible but impractical, implausible, or plausible and probably capable of being implemented?
(Original Post) (http://www.antipope.org/charlie/blog-static/2007/08/anyone_know_if_this_is_for_rea.html)
They're claiming an O(NN) solution to a problem that is NP-complete. According to the abstract:
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.
This is either wrong, or (as Ken MacLeod put it) "we're all doomed". Anyone want to give it a read-through and tell me if it's plausible but impractical, implausible, or plausible and probably capable of being implemented?
(Original Post) (http://www.antipope.org/charlie/blog-static/2007/08/anyone_know_if_this_is_for_rea.html)