Search

Each day an abundance of new data is generated. With that comes the necessity of a data deduplication process within each data project. This need arises due to multiple reasons, some stronger than others: storage efficiency, data linkage, information representation, etc. This article describes the application of distance functions in the process of data deduplication which covers the aforementioned uses cases. [ABSTRACT FROM AUTHOR]

In information theory, linguistics and computer science are important distinct string metrics for measuring the difference between two given strings (sequences). In distinct domains of research are well known the distances of Hamming and Graev-Levenshtein between two strings. For any string distance there are distinct geometrical compute problems. Some of them are as follows: - the calculation of the median of two strings; - the calculation of the weighted means of two strings; - the problem of the convexity of the weighted mean set. In the present article the above geometrical problems are examined for the Hamming and Graev-Levenshtein string distances. [ABSTRACT FROM AUTHOR]

In information theory, linguistics and computer science are important distinct string metrics for measuring the difference between two given strings (sequences). In distinct domains of research are well known the distances of Hamming and Graev between two strings. For any string distance there are distinct geometrical compute problems, one of them being the calculation of the bisector of two strings. In the present article the problem of the bisector of two strings is examined for the Hamming and Graev string distances. [ABSTRACT FROM AUTHOR]

This paper explores some problems related to quasi-metric spaces and Hamming distance. By a space we understand a topological T0-space and let N* = {0, 1, 2, . . . }. In the theory of topological spaces we explore the following problems: Problem 1. Under what conditions is a space quasi-metrizable? Problem 2. Let X be a subspace of a semigroup Z and let d be a quasi-metric on X. What conditions on Z allow for an invariant quasi-metric ρ, which is an extension of d?. In the present article, the following results are presented: Theorem 1. There exists a quasi-metric on a space X with values in N∗ if and only if X is an Alexandroff space. Theorem 2. If Z is the free monoid generated by X, then for any quasi-metric d on X there exists its invariant extension ρ on Z. Theorem 2 will be applied in the study of Hamming, Levenshtein, and other types of distances on strings. [ABSTRACT FROM AUTHOR]

In this article we show that there are invariant distances on the monoid L(A) of all strings closely related to Levenshtein’s distance. We will use a distinct definition of the distance on L(A), based on the Markov - Graev method, proposed by him for free groups. As result we will show that for any quasimetric d on alphabet A in union with the empty string there exists a maximal invariant extension d* on the free monoid L(A). This new approach allows the introduction of parallel and semiparallel decompositions of two strings. In virtue of Theorem 3.1, they offer various applications of distances on monoids of strings in solving problems from distinct scientific fields. The discussion covers topics in fuzzy strings, string pattern search, DNA sequence matching etc. [ABSTRACT FROM AUTHOR]