That revision included people, railways, animals and land alike, even the geometry of farm fields (no acute angles below 70 degrees) and the alignment of trees and shrubs (only on north-south or east-west axes).
If the nested secondary structure is represented as a tree, comparison methods exist for the edit distance between two ordered labeled trees (Zhang and Shasha, 1989) as well as for the alignment of trees (Jiang et al., 1995).
Another interesting question is whether polynomial-time methods for tree alignment of unordered trees, such as the constrained tree edit distance (Zhang, 1996), can be used for aligning fragmentation trees: whereas the restrictions imposed by Zhang (1996) have no sensible interpretation in the context of fragmentation trees, quality of results may still be sufficient for certain applications.
We used the species tree known for the Silene species in the alignment [ 56] instead of the tree built from the alignment because of tree building problems with less than 10 sequences (as in [ 34], see Additional file 5, figure S5).
Description: Theory and practice of systematics, emphasizing issues associated with homology statements and alignments, methods of tree reconstruction, and hypothesis evaluation.
Whereas efficient, polynomial-time algorithms exist for the alignment of ordered trees, the alignment of unordered trees is computationally hard, namely MAX SNP-hard (Jiang et al., 1995).
Let H S A m (T, S) denote the optimal alignment cost of trees T and S in alignment mode m, where m is one of the following modes: Rooted-Ordered, Rooted-Unordered, Unrooted-Ordered or Unrooted-Unordered.
Additional file 6: Fasta of alignment for tree shown in Fig. 2.
Faster algorithms for the computationally demanding alignment of fragmentation trees were presented in [222].
Additional file 4: Figures and alignment of partial trees.
