 
Summary: PREPRINT. In Proc. Scandinavian Workshop on Algorithm
Theory,pages 111121. Springer Verlag, 1990.
Fast Updating of WellBalanced Trees
Arne Andersson
Lund University
Sweden
Tony W. Lai
University of Waterloo
Canada
Abstract
We focus on the problem of maintaining binary search trees with an optimal and nearoptimal
number of incomplete levels. For a binary search tree with one incomplete level and a height
of exactly dlog(n + 1)e, we improve the amortized insertion cost to O(log 3
n). A tree with
2 incomplete levels and a nearoptimal height of dlog(n + 1) + ffle may be maintained with
O(log 2 n) amortized restructuring work per update. The amount of restructuring work is
decreased to O(log n) by increasing the number of incomplete levels to 4, while the height
is still kept as low as dlog(n + 1) + ffle. This yields an improved amortized bound on the
dictionary problem.
Trees of optimal and nearoptimal height may be represented as a pointerfree structure
