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I have a sequence of points $y_1,\ldots,y_n\in \mathbb{R}^3$ and want to approximately minimise $$ \sum_{i=1}^{n-1}|y_{\pi(i)}-y_{\pi(i+1)}| $$ by choosing a permutation $\pi$ of $\{1,\ldots,n\}$. I have a budget of $\mathcal{O}(n\log(n)^p)$ for some $p\in\mathbb{N}$. What would be the best heuristic for this endeavour?

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  • $\begingroup$ You can't minimize a single number. What are you permitting to vary? $\endgroup$ Jun 2, 2017 at 12:12
  • $\begingroup$ Of course you are right. Forgot to mention the permutation. $\endgroup$ Jun 2, 2017 at 16:53

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