Optimal Binary Search Trees with Near Minimal Height
Abstract
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.
Cite
@article{arxiv.1011.1337,
title = {Optimal Binary Search Trees with Near Minimal Height},
author = {Peter Becker},
journal= {arXiv preprint arXiv:1011.1337},
year = {2010}
}