Average Profile of the Generalized Digital Search Tree and the Generalized Lempel-Ziv Algorithm

On Generalized Digital Search Trees with Applicationsto a Generalized Lempel - Ziv

The goal of this research is twofold: (i) to analyze generalized digital search trees, and (ii) to derive the average proole (i.e., phrase length) of a generalization of the well known parsing algorithm due to Lempel and Ziv. In the generalized Lempel-Ziv parsing scheme, one partitions a sequence of symbols from a nite alphabet into phrases such that the new phrase is the longest substring seen...

Average Profile of Generalized Digital Search Trees and the Generalized Lempel-Ziv Algorithm

Average profile and limiting distribution for a phrase size in the Lempel-Ziv parsing algorithm

Wojciech Szpankowskl* Department of Computer Science Purdue University W. Lafayette, IN 47907 U.S.A. Consider the parsing algorithm due to Lempel and Ziv that partitions a sequence of length n into variable phrases (blocks) such that a new block is the shortest substring not seen in the past as a phrase. In practice the following parameters are of interest: number of phrases, the size of a phra...

Traveling Front Solutions to Directed Diffusion Limited Aggregation Digital Search Trees and the Lempel-Ziv Data Compression Algorithm

We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion-limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely, the digital search tree problem in data structures and the Lempel-Ziv algorith...

Asymptotic Behavior of the Height in a Digital Search Tree and the Longest Phrase of the Lempel-Ziv Scheme

Wojciech Szpankowskit Department of Computer Science Purdue University W. Lafayette, IN 47907 U.S.A. spa~cs.purdue.edu We study the height of a digital search tree (DST in short) built from n random strings generated by an unbiased memoryless source (i.e., all symbols are equally likely). We shall argue that the height of such a tree is equivalent to the length of the longest phrase in the Lemp...