Re^5: Travelling problem

> New users, however, may not know how to filter out the mindless nostrums.

Or may be too lazy to express themselves properly, and never improve cause karma whores spoil them with answers? :)

Anyway I learned new things again, I wasn't aware that the "NP-heuristics" are able to guaranty such good results like Christofides does.

Thats impressive, especially cause NP-problems are transformable into each other.

(Though it might not help much, if one needs to know for 100% if two graphs are isomorphic or not.)

Cheers Rolf

( addicted to the Perl Programming Language)

Comment on Re^5: Travelling problem

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Re^6: Travelling problem by educated_foo (Vicar) on Dec 22, 2013 at 13:40 UTC
I wasn't aware that the "NP-heuristics" are able to guaranty such good results like Christofides does. I only knew because I took a course from a guy (EDIT: Bill Cook, who literally wrote the book on the TSP) whose research specialty was the TSP. Another cool thing about it is that you can find good lower bounds on the length (based on the minimum spanning tree length), so you can use those plus a heuristic (i.e. upper bound) to iteratively find the true solution. I have no idea whether "good-enough" solutions to the TSP can be translated to "good-enough" solutions to other NP-complete problems, but that's an interesting thought. Many of the ways of reducing one NP-complete problem to another are fairly bizarre, so solution quality might not translate.	[reply]

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Re^6: Travelling problem
by educated_foo (Vicar) on Dec 22, 2013 at 13:40 UTC

I wasn't aware that the "NP-heuristics" are able to guaranty such good results like Christofides does.

Bill Cook

I have no idea whether "good-enough" solutions to the TSP can be translated to "good-enough" solutions to other NP-complete problems, but that's an interesting thought. Many of the ways of reducing one NP-complete problem to another are fairly bizarre, so solution quality might not translate.

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