Optical Solution For an NP-Complete Problem?

6 writes to let us know that two optical researchers have proposed, as a thought experiment, a novel idea for solving the traveling salesman problem. From 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 N^N 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."

Better solution...

[Anonymous Coward]

I think a couple of gaurd dogs and a shotgun are a good enough method to solve the travelling salesman problem.

I for one

[Mipoti Gusundar]

I for one am welcomming our new briefcase carrying shiny shoes foot in the door encylopadea selling in most efficient manners overloads!

Article is also NP-Complete Problem

[LiquidCoooled]

In order that you can solve the article and produce feasible text in quadratic time you have to use a novel technique of installing a PDF reader.

Obligatory

[Tackhead]

"Nothing to see here. Please move along, but no, no, no, not over that bridge, you idiot! That's another one of those fucking pathological edge cases that invalidates what would have been an otherwise great TSP equivalence proof, and now I have to start all over again! Curse you, Konigsberg, why didn't the Brits and the Russians and the Germans finish you off when you were fair game!"

(Did I mention how much I hated my Computability and Complexity courses when I was in college?)

So (a real comment)...

[LiquidCoooled]

So, to find out the shortest path for a travelling salesman you have to have a travelling Fibre fitter installing cables between all the cities?

What is the optimum path the fibre fitter must take to lay all the cables and reduce his mileage?

First Thoughts

[TheRequiem13]

...gedankenexperiment...

Gasundheit!

GRB explanation

[a.d.venturer]

As pointed out here [antipope.org] "Apparently the method is polynomial in time, but exponential in energy ..."

to which Charles Stross replies "Ah, so that's what the short duration GRBs are!"

Fnord.

Re:Some Reference info

[ZOMFF]

Badonkadonkexperiment [wikipedia.org] ???

Re:Better solution...

[spun]

You don't even need to go that far. In fact, if you don't have an attractive teenage daughter you should be all right. If you do, you simply do not let the traveling salesman sleep anywhere on your property. Or so I've heard.

You've exceeded Slashdot's DMR

[spun]

That joke has too high of a Dennis Miller ratio [snpp.com] even for Slashdot.

Re:So (a real comment)...

[LiquidCoooled]

You just don't get it...
The travelling fibre layer must visit every city from every other city making his journey MUCH longer than the original salesman.
Might be easier just giving the fibre fitter a second moonlighting job as a salesman.

P= NP

[naoursla]

P is equal to NP because processing speed is increasing expoentially. Each year, the amount of processing you can do doubles.

The researchers are just using an expoential number of photons to aid in the processing.

Josie Bauer addressed Travelling Salesman problem

[karlandtanya]

Some time ago.

Solution involved a Farmer's daughter, which she apparently was.

Re:exponential photons == not practical

[RealAlaskan]

... their algorithm would require on the order of 50^50 photons (about 10^85). For comparison, the Sun emits roughly 10^45 photons per second.

So, are you saying that this is a pretty bright idea? Or that it's not so bright?

Mad moderation.

[serviscope_minor]

The parent post is woefully incorrect (just read a wikipedia article on NP completeness). But it is not a troll.

Please, mods use some sense in moderating.

Re:Not the first time this has been proposed

[Climate Shill]

Or to put it a little more excitingly, solving a 26 step problem with 12um photons will take somewhere in the region of 25 megatons.

Which means you would probably have to be pretty desperate for sales.

Re:The run time is wrong

[SamP2]

>I would say they're still looking at an n^n problem unless they can produce an infinite number of photons instantly, and that would damage the equipment

If you can produce an infinite number of photons instantly than I don't think you'd be worried about any kind of equipment.

For starters, try producing an infinite number of photons non-instantly (in a finite period of time), OR try to produce a finite number of photons instantly. Equipment will be the least of your problems.

Re:Parallel computing

[camperdave]

...and Heisenberg says you never will.

He may have said it, but he wasn't certain about it.

Re:Better solution...

[AndersOSU]

If you have a hot daughter odds are you already had a traveling salesman problem, you just didn't know about it.

More precisely, wouldn't you be a German Nazi?

[JimTheta]

Your friendly neighbourbood grammar Nazi

If I had a hard-ass Spanish teacher correcting my Spanish, then I'd call him/her a "Spanish Nazi". So, you know, if you were correcting my German, it stands to follow...

I'm just sayin'.

Congratulations

[Anonymous Coward]

You have discovered an O(n^2) way to determine the shortest path between two cities.

...Although I suspect there may be a slightly faster algorithm.

Re:Parallel computing

[camperdave]

Schrödinger's cat wasn't going to commit to one side or the other until he saw it in action.