Affiliation:
1. Univ. of Freiburg, Freiburg, W. Germany
2. Univ. of Waterloo, Waterloo, Ont., Canada
Abstract
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
External Path Length ≤
N(log
2
N + Δ - log
2
Δ - 0.6623),
where
N
denotes the number of external nodes in the tree and Δ is the difference in length between a longest and shortest path. Then it is proved that this bound is tight up to an
o(N)
term if Δ ≤ √N. If
Δ > √N
, we contstruct binary trees whose external path length is at least as large as
N(log
2
N + Φ(N, Δ)Δ - log
2
Δ -4)
, where
Φ(N, Δ) = 1/(1 + 2(Δ/N))
.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference6 articles.
1. HAMMING R.W. Coding and Information Theory. Prentice-Hall Inc. Englewood Cliffs N.J. 1980. HAMMING R.W. Coding and Information Theory. Prentice-Hall Inc. Englewood Cliffs N.J. 1980.
2. Upper Bounds for the Total Path Length of Binary Trees
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