On the Path Length of Binary Trees

  • Authors:

  • Rolf Klein;Derick Wood

  • Affiliations:

  • -;-

  • Venue:
  • On the Path Length of Binary Trees
  • Year:
  • 1987

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Abstract

We show 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 \[ \mbox{External Path Length}\leq N(\log_2 N+\Delta - \log_2\Delta -0.6623) \] where $N$ denotes the number of external nodes in the tree and $\Delta$ ist the difference in length between a longest and a shortest path. Then we prove that this bound is (almost) achieved if $N$ and $\Delta$ are arbitrary integers that satisfy $\Delta\leq\sqrt{N}$. If $\Delta