- Exponentially Decreasing Number of Operations in Balanced Trees.
- Lars Jacobsen and Kim S. Larsen.
Acta Informatica, 82(4): 57-78, 2005.
While many tree-like structures have been proven to support amortized
constant number of operations after updates, considerably fewer structures
have been proven to support the more general exponentially decreasing number
of operations with respect to distance from the update. In addition, all
existing proofs of exponentially decreasing operations are tailor-made for
specific structures. We provide the first formalization of conditions under
which amortized constant number of operations imply exponentially decreasing
number of operations. Since our proof is constructive, we obtain the
constants involved immediately. Moreover, we develop a number of techniques
to improve these constants.
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