On the Editing Distance Between Trees And Related Problems

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On the Editing Distance Between Trees And Related Problems
Kaizhong Zhang
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I]. In this case DPl(Ti[l(ii) .. I], 0) = D(Ti[l(ii) .. L(p(i)) - 1], 0). Otherwise, we can prune for Ti[l(i;) .. I - 1], giving cost DPl(Ti[Uii).. I], 0)=DRl(Ti[l(ii) .. I - l], 0)-g(Ti[i]-A)}.
Hence the left_initialization is correct.
Now let us consider the general_term_computation.
Lltracomputer Note 122 Page 17 First there are two cases: Case (1): Ti[l(p(i)) .. I] is removed. So, DPl(Ti[l(ii) .. Il, T2[lOi) ••]]) = D(Ti[l(ii) .. L(p(i)) - l], T2[l(j;) •• il) Note: this case is conditional,
... depending on if all the descendants of p(i) are in Ti[l(ii) .. I), i. E. Arewithin(i, !i).
Case (2): Ti[l(p(i)) .. I] is not removed.
Consider the best mapping between T;[l(ii) .. I] and T2[I(ji) ■• j] with a pruning at a node in Ti[l(ii j .. I].
There are three subcases.
subcase 1: i is not in the mapping. In this case, DPl(Ti[l(ii) .. I], T:[l(ji) .. J]) = DPl(Ti[l(ii) .. I - l], T;[l(j:) . - j])-v(Ti[il-, V), subcase 2: j is not in the mapping. In this case, DPl(Ti[Ki. ) .. I], T2[l(ji) ..


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