We study the problem of efficiently retrieving large entries in the product of two given matrices, which arises in a number of data mining and information retrieval tasks. We focus on the setting where the two input matrices are tall and skinny, i.e., with millions of rows and tens to hundreds of columns. In such settings, the product matrix is large and its complete computation is generally infeasible in practice. To address this problem, we propose the LEMP algorithm, which efficiently retrieves only the large entries in the product matrix without actually computing it. LEMP maps the large-entry retrieval problem to a set of smaller cosine similarity search problems, for which existing methods can be used. We also propose novel algorithms for cosine similarity search, which are tailored to our setting. Our experimental study on large real-world datasets indicates that LEMP is up to an order of magnitude faster than state-of-the-art approaches.
This article considers the problem of translation of colloquial phraseology. A comparison of translations into Ukrainian language from the original language. Methods of translation of phraseological units are investigated. Particular attention is paid to Catherine Cusse's novel “A Perfect Future” and its translation into Ukrainian language. The essence of phraseological units, their originality and specificity is revealed. In the article the quality and equivalence of phraseological units translation into Ukrainian language are analysed. This article attempts to reveal the main causes of the translation of phraseological expressions. The relevance of the issue of phraseological translation is proved. The paper studies phraseological units and how they represent the national character of each nation. The emotional aspect has been studied and the impact that it has on the reader or listener. The development of phraseology is analysed. The article discusses French and Ukrainian phraseologisms, their similarities and differences. It has been studied that phraseologisms convey semantic, lexical and grammatical features of language.It was showed that some phraseologies need support and explanation of the text. The main indicator semantic reinterpretation of phraseology is the opposition of literal and figurative value. The direct meaning of phraseological units is practically absent if talk about its etymolog-ical roots, as the basis for its explanation is an unrealistic or imaginary, desirable sit-uation. The article also discusses the problem with the unidirectional approach. It was investigated that rethinking as a form of semantic transformation of phrases is the most common and most productive in French, the newest phraseological units arise as a result of rethinking free phrases. The practical significance of the research results is substantiated. So, the work is devoted to the research of peculiarities of translation into Ukrainian of French phraseological units. This research can be helpful because this work represents a great theoretical value for those who want to take up their future carrier in the field of translations as invaluable reference to the methods and the ways of translation of phraseologisms in everyday life.
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