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PREPRINT. In Proc. Scandinavian Workshop on Algorithm Theory,pages 111121. Springer Verlag, 1990.

Summary: PREPRINT. In Proc. Scandinavian Workshop on Algorithm
Theory,pages 111­121. Springer Verlag, 1990.
Fast Updating of Well­Balanced Trees
Arne Andersson
Lund University
Tony W. Lai
University of Waterloo
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


Source: Andersson, Arne - Department of Information Technology, Uppsala Universitet


Collections: Computer Technologies and Information Sciences