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The rotation distance d(S,T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T.
As well known the rotation distance D S,T) between two binary trees S, T of n vertices is the minimum number of rotations of pairs of vertices to transform S into T.
The restricted rotation distance dR S,T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T, where rotations take place at the root of S, or at the right child of the root.
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However, in the case of two binary trees, the problem is polynomial.
(Cf. blue stragglers) A likely scenario is a collision with a binary star system, or between two binary systems containing white dwarfs.
The MCC represents a Pearson correlation between two binary vectors.
Recently, we have extended our previous approach in (Wu, 2009) to allow computing the pairwise reticulation distance between two rooted binary trees (Wu and Wang, 2010).
For two unrooted binary trees with n ≥ 3 leaves, the R-F score is in the range [0,2 n−6].
The basic data structure is a hierarchical tree of spatial cells, which are either cubic with eight daughters cells (oct-tree) or cuboidal with two daughters (binary tree).
However, Allen and Steel [ 20] showed that it is actually the tree bisection and reconnection (TBR) distance that is being calculated, and in Rodrigues et al. [ 22] the approximation factor was shown to be 4. LatTrans [ 23] calculates the minimum number of SPR operations in the path between two rooted binary phylogenetic trees subject to certain direction of time constraints.
Bordewich and Semple [ 5] established the following characterization which directly relates the rSPR distance to the number of elements in a maximum-agreement forest and is crucial to many algorithms that exactly compute the rSPR distance between two rooted binary phylogenetic trees.
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