in this paper, by applying three functional operators the previous results on the(poisson) variance of the external profile in digital search trees will be improved. we study the profile built over $n$ binary strings generated by a memoryless source with unequal probabilities of symbols and use a combinatorial approach for studying the poissonized variance, since the probability distribution of...

Digital search is expressed by the digital search tree which considers a part of keys as transitions. Therefore, it is frequently used for various applications, such as natural language dictionaries because of being dependent on the key length for search processing. There is the compressed digital search tree which compressed the one-way branches after the leaf and reduces nodes on digital sear...

Author(s): R. Kazemi and M. Q. Vahidi-Asl Abstract: What today we call digital search tree (DST) is Coffman and Eve’s sequence tree introduced in 1970. A digital search tree is a binary tree whose ordering of nodes is based on the values of bits in the binary representation of a node’s key. In fact, a digital search tree is a digital tree in which strings (keys, words) are stored directly in in...

This paper presents digital search trees, a binary tree data structure that can produce well-balanced trees in the majority of cases. Digital search tree algorithms are reviewed, and a novel algorithm for building sorted trees is introduced. It was found that digital search trees are simple to implement because their code is similar to the code for ordinary binary search trees. Experimental eva...

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 ...

This paper studies the asymptotics of the variance fOf the internal path length in a. symmetric digital search tree. The problem was open up to now. We prove that COf the binary digital search tree the variance is asymptolically equal 10 0.26600 ... · N + N6(1og2 N) where N is the number of stored records and 6(:z:) is a. periodic function of mean zero and a very small amplitude. This result im...

Digital Search Trees (DST) are one of the most popular data structures storing keys, usually represented by strings. The profile of a digital search tree is a parameter that counts the number of nodes at the same distance from the root. It is a function of the number of nodes and the distance from the root. Several, if not all, tree parameters such as height, size, depth, shortest path, and fil...

This paper smdies the average complexity of digital search trees from the successful search point of view. The average value of the successful search is used to evaluate the search time for a given record, the number of comparisons to insert a record, etc. The average value, however, is rather a poor measure and the need for higher moments of the successful search is obvious. For example, the v...

We consider the continuous-time version of random digital search tree, and construct a coupling with border aggregation model as studied in Thacker Volkov (Ann. Appl. Probab. 28 (2018) 1604–1633), showing relation between height tree time required for aggregation. This carries over to corresponding discrete-time models. As consequence we find very precise asymptotic result aggregation, using re...

A digital search tree (DST) – one of the most fundamental data structures on words – is a digital tree in which keys (strings, words) are stored directly in (internal) nodes. The profile of a digital search tree is a parameter that counts the number of nodes at the same distance from the root. It is a function of the number of nodes and the distance from the root. Several tree parameters, such ...