№ 59-4 (том 1): ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, Февраль, 2025
Научно-образовательные статьи

UNDERSTANDING MATROIDS: A KEY TO COMBINATORIAL OPTIMIZATION

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  • Ovezov Khalmukhamed Amanmukhamedovich,
  • Amannazarova Ogulnyyaz Amandurdyeva
Ovezov Khalmukhamed Amanmukhamedovich
Oguz han Engineering and Technology university of Turkmenistan. Ashgabat, Turkmenistan
Amannazarova Ogulnyyaz Amandurdyeva
Oguz han Engineering and Technology university of Turkmenistan. Ashgabat, Turkmenistan

Опубликован 25.03.2025

Как цитировать

Kh.A. Ovezov, & O.A. Amannazarova. (2025). UNDERSTANDING MATROIDS: A KEY TO COMBINATORIAL OPTIMIZATION. ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, 59-4 (том 1). https://mpcareer-google.ru/index.php/journal/article/view/1241

Аннотация

Matroids are fundamental structures in combinatorial mathematics that generalize the concept of linear independence. They provide a powerful framework for solving optimization problems, designing efficient algorithms, and understanding the properties of graphs, networks, and geometric configurations. From greedy algorithms to machine learning, matroids underpin many modern computational techniques. This article explores why matroids matter, how to study them, and their role in advancing mathematics and computer science. 

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Библиографические ссылки

  1. Book: "Matroid Theory" by James Oxley — A comprehensive introduction to matroid axioms and applications.
  2. Online Course: "Combinatorial Optimization" on Coursera — Covers matroids, greedy algorithms, and network flows.
  3. Research Paper: "Matroids and the Greedy Algorithm" by Jack Edmonds — Seminal work linking matroids to algorithmic efficiency.
  4. Textbook: "Introduction to Algorithms" by Cormen et al. — Includes sections on matroid-based greedy approaches.