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List of publications on a keyword: «теория графов»

  • Boolean functions and their applications in machine learning: from logical rules to explicable artificial intelligence

    Proceeding
    Relevant problems of modern science and education
    Authors:
    Фоменко Артём Викторович, Ilia V. Baranov, Aleksandr E. Sergeev
    Work direction:
    Инновационный опыт в науке и образовании в современном обществе
    Abstract:
    Automated scheduling is an applied task of discrete optimization, where graph models and combinatorial algorithms directly affect the quality of educational solutions. The article considers the schedule as a combinatorial optimization problem: from constructing a conflict graph and reducing it to coloring to hybrid schemes combining mathematical programming (MIP), SAT/SMT approaches and evolutionary methods. Special attention is paid to modern open data and tools: ITC 2019 instances (UniTime) and libraries for real implementations. The results of Russian research demonstrating the effectiveness of SMT solvers for generating the initial schedule and modifications of genetic algorithms for optimizing multi-level programs are presented. Based on the review, a practical "pipeline" of scheduling is proposed: decomposition by components of the conflict graph, obtaining a correct basic solution, and subsequent optimization based on soft constraints. The material is focused on the tasks of dig
    Keywords:
    machine learning, discrete mathematics, logical functions, explicable AI, transparent models, classification rules, DNF, interpretability, RIPPER algorithm, analytics in education, Russian developments in XAI

  • The Mathematics of Delivery: How Graph Theory Organizes Urban Routes

    Proceeding
    Socio-Economic Processes of Modern Society
    Author:
    Папазян Андрей Суренович
    Work direction:
    Социально-экономические процессы в обществе
    Abstract:
    This article explores the practical application of discrete mathematics and graph theory methods in modern delivery systems. Using the example of an everyday service - food ordering - it demonstrates how abstract mathematical concepts are transformed into effective algorithms that optimize logistics processes.
    Keywords:
    optimization, graph theory, discrete mathematics, routing algorithms, delivery logistics, traveling salesman problem, time windows, NP-hard problems, urban infrastructure, navigation systems

  • Teoriia grafov kak instrument analiza ekonomicheskikh i upravlencheskikh protsessov

    Proceeding
    Strategies of Sustainable Development: Social, Law and External-economic Aspects
    Authors:
    Aram A. Tutoian, Karen A. Tutoian, Aleksandr E. Sergeev
    Work direction:
    Общие вопросы экономических наук
    Abstract:
    The article discusses the application of graph theory to modeling and analysis of complex systems in economics and management. The relevance of the study is due to the increasing complexity of the relationships between economic agents, logistics hubs, financial flows and management structures. The paper presents the basic concepts of graph theory adapted to applied problems, and also shows the mechanisms of their use in the analysis of supply chains, organizational hierarchies, project management and corporate networks. Based on generalized models, it is demonstrated how graph representations make it possible to identify bottlenecks, assess the stability of systems, and optimize decision-making processes. The results obtained emphasize the interdisciplinary value of discrete mathematics in modern socio-economic research.
    Keywords:
    optimization, graph theory, economic networks, management structures, supply chains, discrete mathematics, analysis of complex systems
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