Optimal Binary Search Trees with Near Minimal Height
- Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let h_min(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal binary search tree with near minimal height, i.e.\ with height h <= h_min(n) + Delta for some fixed Delta. It is shown, that for any fixed Delta optimal binary search trees with near minimal height can be constructed in time O(n^2). This is as fast as in the unrestricted case. So far, the best known algorithms for the construction of height-restricted optimal binary search trees have running time O(L n^2), whereby L is the maximal permitted height. Compared to these algorithms our algorithm is at least faster by a factor of log n, because L is lower bounded by log n.
Document Type: | Preprint |
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Language: | English |
Author: | Peter Becker |
DOI: | https://doi.org/10.48550/arXiv.1011.1337 |
ArXiv Id: | http://arxiv.org/abs/1011.1337 |
Publisher: | arXiv |
Date of first publication: | 2010/11/05 |
Departments, institutes and facilities: | Fachbereich Informatik |
Dewey Decimal Classification (DDC): | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
Entry in this database: | 2015/04/02 |