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arXiv · 1304.7604

Combining Binary Search Trees

Erik D. Demaine·John Iacono·Stefan Langerman·Özgür Özkan
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Abstract

We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any "well-behaved" bound on the running time of the given BSTs, for any online access sequence. (A BST has a well behaved bound with $f(n)$ overhead if it spends at most \bigoh{f(n)} time per access and its bound satisfies a weak sense of closure under subsequences.) In particular, we obtain a BST data structure that is \bigoh{\log\log n} competitive, satisfies the working set bound (and thus satisfies the static finger bound and the static optimality bound), satisfies the dynamic finger bound, satisfies the unified bound with an additive \bigoh{\log\log n} factor, and performs each access in worst-case \bigoh{\log n} time.

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Erik D. Demaine, John Iacono, Stefan Langerman, Özgür Özkan. 2013-04-29. Combining Binary Search Trees. https://arxiv.org/abs/1304.7604

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