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...

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 o...

Consider a tree partitioning process in which n elements are split into b at the root of a tree ( b a design parameter), the rest going recursively into two subtrees with a binomial probability distribution. This extends some familiar tree data structures of computer science like the digital trie and the digital search tree. The exponential generating function for the expected size of the tree ...

Duplicates embedding is one of the most frequently used type of digital image change. The copy-move procedure includes copying an image fragment from one part and pasting it to another part of the same image. Moreover, this fragment can be changed using some transformations, like affine or contrast enhancement. Existing copy-move detection methods consist of two main steps: feature calculation ...

چکیده شناسایی رقومی خاک ها بهعنوان ابزاری برای ایجاد اطلاعات مکانی خاک، راه حل هایی برای نیاز رو به افزایش نقشه های خاک با تفکیک مکانی بالا را تأمین می کند. بنابراین، باید روش های جدید بهمنظور بهدست آوردن اطلاعات مکانی خاک با تفکیک مکانی بالا توسعه پیدا کند. به همین منظور مطالعه ای جهت پیش بینی کلاس های خاک با استفاده از مدل های رگرسیونی در منطقه زرند کرمان طراحی گردید. در این مطالعه، مدل های ر...

The total Steiner k-distance and the k-th total path length are the sum of the size of Steiner trees and ancestor-trees over sets of k nodes of a given tree, respectively. They are useful statistics with many applications. Consequently, they have been analyzed for many different random trees, including increasing tree, binary search tree, generalized m-ary search tree and simply generated trees...

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. Such trees find myriad of applications from the popular LempelZiv’78 data compression scheme to distributed hash tables. The profile of a DST measures the number of nodes at the same distance from the root; it is a functio...

Mathematical content are widely contained by digital document, but major search engines fail to offer a way to search those structural content effectively, because traditional IR methods are deficient to capture some important aspects of math language. In this paper, we propose a similarity-search method for LTEX math expressions trying to provide a new idea to better search math content. Our a...

The digital search tree (dst) plays a central role in compression algorithms, of Lempel-Ziv type. This important structure can be viewed as a mixing of a digital structure (the trie) with a binary search tree. Its probabilistic analysis is thus involved, even in the case when the text is produced by a simple source (a memoryless source, or a Markov chain). After the seminal paper of Flajolet an...