Biased finger trees and three-dimensional layers of maxima: (preliminary version)

We present a method for maintaining biased search trees so as to support fast finger updates (i.e., updates in which one is given a pointer to the part of the tree being changed). We illustrate the power of such biased finger trees by showing how they can be used to derive an optimal <italic>O</italic>(<italic>n</italic>log<italic>n</italic>) algorithm for the 3-dimensional layers-of-maxima problem and also obtain an improved method for dynamic point location.

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