A fast digital search algorithm using a double‐array structure

Abstract

AbstractThis paper presents an efficient digital search algorithm by introducing a new internal array structure called a double‐array that combines the fast access of a matrix form with the compactness of a list form. Each arc of a digital search tree called a DS‐tree can be computed from the double‐array in O(1) time; that is, the worst‐case time complexity for retrieving a key becomes O(k) for the length k of that key. The double‐array is modified to make the size compact while maintaining fast access and algorithms for retrieval, insertion and deletion are presented. Suppose that the size of the double‐array is n + cm, where n is the number of nodes of the DS‐tree, m is the number of input symbols, and c is a constant depending on each double‐array. Then it is proved theoretically that the worst‐case times of deletion and insertion are proportional to cm and cm2, respectively, independent of n. From the experimental results of building the double‐array incrementally for various sets of keys, it is shown that the constant c has an extremely small value, ranging from 0.17 to 1.13.