Efficient comparison of heterogeneous tabular datasets is difficult when sources are unknown or weakly documented. We address this problem by introducing a unified, type-aware framework that builds compact data represen- tations (CDRs)—concise summaries sufficient for downstream analysis—and a corresponding similarity graph (and tree) over a data corpus. Our novelty is threefold: (i) a principled vocabulary and procedure for constructing CDRs per variable type (factor, time, numeric, string), (ii) a weighted, type-specific similarity metric we call Data Information Structural Similarity (DISS) that aggregates distances across heterogeneous summaries, and (iii) an end-to-end, cloud-scalable real- ization that supports large corpora. Methodologically, factor variables are summarized by frequency tables; time variables by fixed-bin histograms; numeric variables by moment vectors (up to the fourth order); and string variables by TF–IDF vectors. Pairwise similarities use Hellinger, Wasserstein (p=1), total variation, and L1/L2 distances, with MAE/MAPE for numeric summaries; the DISS score combines these via learned or user-set weights to form an adjacency graph whose minimum-spanning tree yields a similarity tree. In experiments on multi-source CSVs, the approach enables accurate retrieval of closest datasets and robust corpus-level structuring while reducing storage and I/O. This contributes a repro- ducible pathway from raw tables to a similarity tree, clarifying terminology and providing algorithms that practitioners can deploy at scale.

Кластерний аналіз графових даних є важливою задачею в статистиці та машинному навчанні, особливо при обробці великорозмірних мереж та складних структур даних у контексті Big Data. Визначення оптимальної кількості кластерів для графів з різними розподілами елементів матриці суміжності в кластерах та поза ними становить актуальну проблему, що потребує розробки ефективних математичних підходів та алгоритмів для аналізу масивів великих даних.Метою роботи є дослідження спектральних властивостей стохастичних матриць графів з випадковими елементами та розробка методу визначення оптимальної кількості кластерів для випадку розподілів елементів матриці суміжності з важкими хвостами, у випадку відсутності скінченного математичного сподівання, що є притаманним для задач Big Data аналітики.Методологія дослідження базується на аналізі спектральних властивостей стохастичної матриці графу. Розглянуто випадок незалежних однаково розподілених елементів Aij з розподілами з важкими хвостами. Запропоновано чотири гіпотези щодо кластерної структури графу та досліджено збіжність власних значень матриці P за умови, що елементи матриці суміжності незалежні та однаково розподілені.Наукова новизна отриманих результатів полягає в знаходженні достатніх умов про асимптотику власних значень стохастичних матриць, а також у формулюванні критерію визначення оптимальної кількості кластерів kopt для графів, що узагальнює відомі результати на випадок розподілів з важкими хвостами, характерних для Big Data.Висновки. Розроблений підхід дозволяє ефективно визначати оптимальну кількість кластерів навіть для випадку розподілів з важкими хвостами. Експериментальне моделювання підтвердило точність запропонованого критерію при різних співвідношеннях розподілів матриці суміжності в кластерах та поза ними, що демонструє практичну застосовність отриманих теоретичних результатів.

The article is devoted to the development and theoretical justification of a stochastic analytical model for determining the saturation threshold (ρsat) of multi-channel virtualized network functions (VNF) within the framework of Network Functions Virtualization (NFV) technology. The proposed model is based on the classical M/M/k queuing theory and the exact Erlang C formula, which makes it possible to account for the stochastic nature of telecommunication traffic, randomness of packet arrivals, and probabilistic properties of service processes. Unlike heuristic approaches commonly applied in practice, the model provides mathematically grounded threshold values that ensure a balance between resource utilization efficiency and service quality. To solve the nonlinear equation C(k, ρsat) = Cmax, an efficient numerical algorithm based on the bisection method is proposed. It enables the determination of the maximum allowable channel utilization coefficient and the corresponding traffic intensity λsat. The study thoroughly investigates the nonlinear sensitivity of the system to load depending on the number of parallel channels k, analyzes the effects of horizontal scaling, and considers an extended M/M/k/K model with a limited queue. Based on the conducted calculations, practical recommendations are developed for selecting ρsat and buffer size for typical network functions such as vRouter, vFirewall, vLoadBalancer, vCPE, and DPI/vCGNAT.The adequacy of the model has been validated by comparison with results of discrete-event simulation in the ns-3 environment. The relative error of analytical calculations did not exceed 4,8% across a wide range of loads, which confirms the high accuracy and practical applicability of the proposed approach. Thus, the model fills an important niche in the design and operation of NFV infrastructures for telecom operators, enabling a transition from rough empirical rules (“no more than 70–80% CPU”) to precise, mathematically justified threshold values. This contributes to improved efficiency of computational resource utilization, reduced risk of overload, and guaranteed Quality of Service (QoS) for end users.

The work explores the asymptotic properties of large-dimensional stochastic matrices N under the condition of independence of matrix elements or rows (columns). An analysis of the main properties of eigenvalues of stochastic matrices is conducted. The work is dedicated to investigating the asymptotic characteristics of random matrices under the absence of the second moment and also considers the presence of "heavy tails" in the corresponding transitions in the adjacency matrices of the respective graph. The main result of the work is formulated in terms of the transition matrix of a discrete Markov chain and its eigenvalues. In proving the theorem, a non-degenerate Markov chain is considered, describing a mathematical model of random processes that do not change over time with known transition probabilities between states and a corresponding stochastic matrix P, one of whose eigenvalues is unity, and all eigenvalues of the stochastic matrix do not exceed it in absolute value. The proof of this fact follows from the Perron–Frobenius theorem, which concerns the properties of positive matrices and their eigenvalues. Thus, the theorem considered manages to expand the class of random matrices A for which convergence of eigenvalues of the matrix can be applied under the conditions imposed on the elements of the adjacency matrix. Moreover, the imposed conditions are relaxed compared to classical results, where the existence of a finite second moment for the elements of the adjacency matrix is required. This result generalizes both classical results for the normal distribution and similar results of other authors. The obtained result can be used in graph clustering problems to choose the optimal number of clusters, namely, they can be applied to determine the optimal number of clusters in a Grid system, complex networks, in investigations of the structure of the web space, etc.

As data processing volumes grow in various fields, the demand for applications capable of efficiently managing, processing, and transforming large amounts of information is also increasing. Modern approaches to storing and processing large amounts of data are primarily based on universal text formats, such as CSV and JSON. Their prevalence can be explained by their compatibility with a wide range of software tools and ease of integration. These formats are inefficient when dealing with massive volumes of data, particularly when scaling systems or executing analytical queries. The lack of built-in compression, row structure, and metadata leads to significant time and computing resources, which creates a conflict between the requirements for speed and cost-effectiveness of processing and the technical capabilities of traditional text formats. Columnar storage formats, such as Parquet and ORC, offer an alternative. They employ a compact structure tailored for quick analytical queries in distributed computing settings. Effective coding, indexing, and built-in compression techniques considerably lower data sizes and speed up processing. This research aims to develop and experimentally verify the technology of automated data conversion from inefficient text formats to Parquet and ORC formats using Apache Airflow and Amazon EMR. The proposed architecture involves creating a cloud pipeline that performs data conversion and subsequent storage in formats focused on analytical workloads. The system uses Apache Airflow for process orchestration, Amazon EMR and Apache Spark for distributed processing, AWS S3 as scalable storage, AWS Glue for metadata management, and Amazon Athena for SQL access to transformed data. This approach solves performance problems by offering a flexible, reliable, cost-effective solution that adapts to different work scenarios and workloads.