On the upper bound on the rotation distance of binary trees
Information Processing Letters
Efficient lower and upper bounds of the diagonal-flip distance between triangulations
Information Processing Letters
Note: Refined upper bounds for right-arm rotation distances
Theoretical Computer Science
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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. We introduce the new operation of chain rotation on a tree, involving two chains of vertices, that requires changing exactly three pointers in the data structure as for a standard rotation, and define the corresponding chain distanceC(S,T). As for D(S,T), no polynomial time algorithm to compute C(S,T) is known. We prove a constructive upper bound and an analytical lower bound on C(S,T) based on the number of maximal chains in the two trees. More precisely we prove the general upper bound C(S,T)=