Exponentially Decreasing Number of Operations in Balanced Trees
by Lars Jacobsen, Kim S. Larsen
ftp://ftp.imada.sdu.dk/pub/papers/pp-2000/12.ps.gz
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Abstract:
Requiring only very few and natural conditions to be fullled for operations on tree-like structures, we prove that amortized constant-time operations imply that the number of operations carried out at a given distance from the leaves decreases exponentially in that distance. This means that with very few extra arguments, many structures for which amortized constant time operations have been established can now claim this stronger and, in some applications, more useful property.
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