Coding and information theory (2nd ed.)
Coding and information theory (2nd ed.)
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Upper Bounds for the Total Path Length of Binary Trees
Journal of the ACM (JACM)
On the Maximum Path Length of AVL Trees
CAAP '88 Proceedings of the 13th Colloquium on Trees in Algebra and Programming
On the Path Length of Binary Trees
On the Path Length of Binary Trees
Drawing Trees Nicely with TeX
Mathematical Properties of the Deep Coalescence Cost
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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It is shown that the external path length of a binary tree is closely related to the ratios of means of certain integers and establish the upper bound ExternalPathLength≤N log2N+D -log2D -0.6623, where N denotes the number of external nodes in the tree and D is the difference in length between a longest and shortest path. Then it is proved that this bound is tight up to an ON term if D≤N . If DN , we contstruct binary trees whose external path length is at least as large as Nlog2 N+fN,D D-log2 D-4 , where fN,D=1/ 1+2D/N .