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INTRO: I have 15 points forming a graph G in R^3. Call permutations of the form {-4,-3,...3,4}^3 \ V{G} (vertex set of G):= "Candidate set". Each point in the candidate set is added to the Graph and a metric is checked, if the metric spits out a 'True', then I add it to a list of "Successes". Of the candidate points, something like 5% give 'True', and are added. I now have 0.05 * |candidate_points| # of points to check. A decision tree is made in this way, Since I start with 15, I have ~100 'True' options for growing it to 16. But, there are 'dead ends', wherein if I choose a certain point that gave 'True', it will not grow to anything greater than 17. But, there are certain longer paths that are found when I randomize things, and can get to 22 even 23. But i'm confident there are even longer paths down the tree.

PROBLEM: I eventually step up to permutations in R^6, R^7. And things blow up quickly. Is there a neater way for me to sample the candidate points other than bruting it or just doing random.shuffle on the set? Is there a faster algorithm for this?

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  • $\begingroup$ Welcome to CS.SE! I confess I don't understand what you're trying to do. What is your ultimate goal? Why are you building a decision tree? How is the decision tree used? How does adding points using the method you describe help build a decision tree? I'm completely lost. Can you give a self-contained specification of the algorithmic task you are trying to solve? What are the inputs? What is the desired output? Then, describe what approaches you have considered, and why you have rejected them. It'd be useful if you could edit your question accordingly. $\endgroup$ – D.W. Jul 11 '16 at 8:18
  • $\begingroup$ Is this intended to be the same question as math.stackexchange.com/q/1855316/14578, or is it different? Note that we don't want you to cross-post the same question on two different SE sites (but if you have two different questions it is fine to post each on its own SE site). $\endgroup$ – D.W. Jul 11 '16 at 8:19

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