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So this is a question within a bigger question for which I've reduced to this so far:

If I have a tree (phylogenetic) with known weights for leaves, how would I find the weights for all internal nodes such that the sum of the differences between the weights of two endpoints of edges is minimized?

  • I.e. Given a tree $T$ with $n$ leaves with weights $D_1,\ldots,D_n$ respectively. Assign;

    a weight $D_u$ to each internal node $u = n+1,\ldots,2n-1$ such that $\sum_{(u,v) \in E(T)} (D_u-D_v)$ is minimized.

If it helps, it might be similar to the Sankoff algorithm or so. Thanks!

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  • $\begingroup$ You can use LaTeX to typeset mathematics, rather than doing it manually with various tricks (and non-tricks). A couple of users have edited to show you how; we also have a brief tutorial $\endgroup$ – Apass.Jack Oct 23 '18 at 14:33
  • $\begingroup$ Do you mean the absolute value of the difference between $D_u$ and $D_v$ , $|D_u-D_v|$ instead of $D_u-D_v$? Minimizing (the sum of) the difference does not make sense, since $(v,u)$ is the same edge as $(u,v)$. $\endgroup$ – Apass.Jack Oct 23 '18 at 15:01

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