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I am implementing the dynamic programming algorithm for computing tree alignment distance as described in "Alignment of trees — an alternative to tree edit". But I got stuck in lemma 3 on page 141 (page 5 of pdf). The notations are given at the beginning of section 2. The last case in lemma 3 says

formula

However, there is no recurrence formula given to compute . How did we obtain this?

I don't think the following holds either: x?

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    $\begingroup$ Welcome to CS.SE! I think you should be asking a more basic question: what is the definition of $F_1[i_s]$? Anyway, a good way to approach this is probably to try to prove the lemma yourself. Do you understand the proofs of the other cases (Case 1, 2, 2.1, 2.2, 2.3)? I suggest studying those, then trying to apply a similar methodology to reason about that case (Case 3) and try to derive a formula on your own. Also, I don't know what your final line is referring to ("I don't think..."), but in any case, we prefer that you ask only one question per post. $\endgroup$ – D.W. Mar 22 '17 at 21:27
  • $\begingroup$ $F_1[i_s]$ is actually defined in section 2 as the first forest under node $i_s$. My concern was that the recurrence relationship are of forests starting from $i_1, j_1$ but we need $D(F_1[i_s], F_2[j_k, j_t])$ which start with $j_k$ and not $j_1$. Anyhow, thanks for your help :) $\endgroup$ – spin Mar 22 '17 at 22:16
  • $\begingroup$ OK, got it -- I overlooked that. Thank you for the explanation. $\endgroup$ – D.W. Mar 22 '17 at 22:27
  • $\begingroup$ Could you give some more context, please? People shouldn't have to go find section2 of a document that you've liked just to figure out what you're even talking about. Also, please replace the images of equations with LaTeX. $\endgroup$ – David Richerby Mar 23 '17 at 12:18
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If I understand the paper correctly (and I might not), the solution seems to be described in Section 2.2 of the paper. It says "we have to compute $D(F_1[i],F_2[j_s,j_t])$..." and then it goes on to describe a strategy for doing so (namely, the Procedure 1, as described in Figure 2).

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