Digital Search Trees Revisited

Several algorithms have been proposed which build search trees using digital properties of the search keys. A general approach to the study of the average case performance of such algorithms is discussed, with particular attention to the analysis of the digital search tree structures of Coffman and Eve. Specifically, the method leads to the solution of a problem left open by Knuth, finding the average number of nodes in digital search trees with both sons null. The paper may be of interest as a survey and tutorial treatment of the analysis of the three primary digital tree search methods: digital search trees, radix search tries, and Patricia tries. 1. Introduction. A fundamental problem in computer science is the so-called dictionary problem, where various operations, chiefly search and insert, are to be performed on a set of records possessing key values. To insert a record is to store it away for later retrieval; to search is to find a previously stored record with a given key value. The binary search tree is an elementary data structure for solving this