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I have 80 nodes and I need to find a cycle of length 40 from these, while keeping the distance traveled by the cycle to a minimum. Some nodes cannot directly connect, they're in specific areas and I can only travel from one area to another, not within one area.

I'm just asking in general here, what kind of techniques can I use to get the best (shortest) possible cycle of 40 nodes? So far I've written a basic substitution optimizer and just a greedy DFS. I'm wondering what would be the best approach for me to start on now?

rptynan
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  • I guess you could create an 80×80 matrix and take its 40th power, that would at least tell you how many cycles there are and which their starting nodes are. – Neil Oct 14 '12 at 00:00
  • What exactly do you mean take its 40th power? – rptynan Oct 14 '12 at 21:24
  • Matrix multiplication allows you to take the 40th power of a square matrix. I think in this special case you don't even have to worry about associativity so you can just multiply the 32nd power by the 8th power. – Neil Oct 14 '12 at 21:28

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