Performance of Height-Balanced Trees
This paper presents the results of simulations
that investigate the performance of height-balanced 
(HB[k]) trees.  It is shown that the only statistic
of HB[1] trees (AVL trees) that is a function of 
the size of the tree is the time to search for an item
in the tree.  For sufficiently large trees, the 
execution times of all procedures for maintaining HB[1]
trees are independent of the size of the tree. 
 In particular, an average of .465 restructures are required
per insertion, with an average of 2.78 nodes 
revisited to restore the HB[1] property; an average of
 .214 restructures are required per deletion, with 
an average of 1.91 nodes revisited to restore the HB[1]
property.  Moreover,the execution times of procedures 
for maintaining HB[k] trees, for k>1, are also independent
of the size of the tree except for the average 
number of nodes revisited on a delete operation in
order to restore the HB[k] property on trace back. 
 The cost of maintaining HB[k] trees drops sharply as the
allowable imbalance (k) increases.  Both analytical 
and experimental results that show the cost of maintaining
HB[k] trees as a function of k are discussed.
CACM January, 1976
Karlton, P. L.
Fuller, S. H.
Scroggs, R. E.
Kaehler, E. B.
