## Binary Search Trees of Almost Optimal Height (1990)

Venue: | ACTA INFORMATICA |

Citations: | 11 - 1 self |

### BibTeX

@MISC{Andersson90binarysearch,

author = {Arne Andersson and et al.},

title = {Binary Search Trees of Almost Optimal Height},

year = {1990}

}

### Years of Citing Articles

### OpenURL

### Abstract

First we present a generalization of symmetric binary B-trees, SBB(k)- trees. The obtained structure has a height of only \Sigma (1 + 1k) log(n + 1)\Upsilon, where k may be chosen to be any positive integer. The maintenance algorithms require only a constant number of rotations per updating operation in the worst case. These properties together with the fact that the structure is relatively simple to implement makes it a useful alternative to other search trees in practical applications. Then, by using an SBB(k)-tree with a varying k we achieve a structure with a logarithmic amortized cost per update and a height of log n + o(log n). This result is an improvement of the upper bound on the height of a dynamic binary search tree. By maintaining two trees simultaneously the amortized cost is transformed into a worstcase cost. Thus, we have improved the worst-case complexity of the dictionary problem.