Median split trees

Abstract

Split trees are a new technique for searching sets of keys with highly skewed frequency distributions. A split tree is a binary search tree each node of which contains two key values—a node value which is a maximally frequent key in that subtree, and a split value which partitions the remaining keys (with respect to their lexical ordering) between the left and right subtrees. A median split tree (MST) uses the lexical median of a node's descendents as its split value to force the search tree to be perfectly balanced, achieving both a space efficient representation of the tree and high search speed. Unlike frequency ordered binary search trees, the cost of a successful search of an MST is log n bounded and very stable around minimal values. Further, an MST can be built for a given key ordering and set of frequencies in time n log n , as opposed to n 2 for an optimum binary search tree. A discussion of the application of MST's to dictionary lookup for English is presented, and the performance obtained is contrasted with that of other techniques.