Abstract
This chapter focuses on the top-down algorithm for constructing nearly optimal lexicographic tree, wherein, a lexicographic tree is a binary search tree. The binary search tree has been proposed as a data structure for lists of names which must be both searched and updated frequently. A binary search tree is a rooted, ordered tree such that the out-degree of every node is two foran internal nodes or zero for a leaf. If there are N internal nodes, there are 2N edges and N+ 1 leaves. Each internal node is associated with one name in a set of lexicographically ordered names, A 1 < A 2 < ··· <AN. A special case of the lexicographic tree occurs when all the βi are zero. In this case, only the names A 1, A 2, …, AN would be used to search the tree and all searches would be successful, that is, terminate at an internal node.
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