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Using modular decomposition technique to solve the maximum clique problem
P. 121–131.
Utkina I. E.
In this article we use the modular decomposition technique for exact solving the weighted maximum clique problem. Our algorithm takes the modular decomposition tree from the paper of Tedder et. al. and finds solution recursively. Also, we propose algorithms to construct graphs with modules. We show some interesting results, comparing our solution with Ostergards algorithm on DIMACS benchmarks and on generated graphs.
In book
Valery A. Kalyagin, Panos M. Pardalos, Oleg Prokopyev, Irina Utkina Vol. 247. , Springer, 2018.
Smirnov A., Экономика региона 2022 Т. 18 № 1 С. 133–145
The nature and intensity of migration processes are constantly changing. Demographic statistics are not suitable for obtaining up-to-date information and making timely decisions in the field of demographic and social policy. Thus, digital demography is becoming increasingly important, as this area of population research uses new methods and data sources resulting from the Internet expansion ...
Added: March 18, 2026
Smirnov A., Демографическое обозрение 2025 Т. 12 № 2 С. 35–68
The article summarizes the application of the network approach to the analysis of migration flows in Russia from the late Soviet period to 2023. Eleven datasets on international, interregional and intermunicipal migration flows were compiled. The data sources include the 1989, 2002, 2010, 2020 (2021) population censuses, vital statistics for 2015-2023 and the “digital traces” ...
Added: March 18, 2026
Дистель Р., М.: МЦНМО, 2024.
С момента выхода первого издания на английском языке в 1997 году книга известного математика, профессора Гамбургского университета Рейнгарда Дистеля стала основным учебником по теории графов во многих университетах, выдержав к настоящему времени пять изданий, перевод последнего из которых предлагается читателю. Уникальность учебника в его глубине при относительно небольшом объёме: в книге найдутся задачи как доступные ...
Added: January 25, 2026
Shestakova L. V., Семакин И. Г., Залогова Л. А. et al., М.: Просвещение, 2024.
The textbook is intended for studying computer science at the basic level in the 9th grade of general education organizations. The textbook contains the theoretical course material, questions and assignments for consolidation of knowledge. At the end of each chapter, the system of basic concepts of this chapter is presented schematically. The textbook is part ...
Added: July 7, 2025
Кочкаров А. А., Яцкин Д. В., Кочкаров Р. А., М.: КноРус, 2021.
Содержит основные сведения и задачипо теории графов, а также описание ключевых моделей, связанных с графами и сетями, с рассмотрением прикладных аспектов их применения. Для студентов бакалавриата, обучающихся по направлению "Экономика". ...
Added: March 8, 2025
Арутюнов Г. А., Avdoshin S. M., Труды Института системного программирования РАН 2024 Т. 36 № 4 С. 69–80
Although software development is mostly a creative process, there are many scrutiny tasks. As in other industries, there is a trend for automation of routine work. In many cases, machine learning and neural networks have become a useful assistant in that matter. Programming is not an exception: GitHub has stated that Copilot is already used ...
Added: November 1, 2024
Velikonivtsev F., Mironov M., Prokhorenkova L., , in: 38th Conference on Neural Information Processing Systems (NeurIPS 2024).: [б.и.], 2024. P. 57993–58022.
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the problem of generating structurally diverse graphs has not been explored in the literature. In this paper, ...
Added: October 15, 2024
Lyskov D., Доценко В., Келти А., Algebraic Combinatorics 2024 Vol. 7 No. 3 P. 801–842
Added: July 1, 2024
Ayzenberg A., Beketov M., Magaj G., / Series arxiv:math.AT "arxiv Algebraic Topology". 2023.
In this paper we study the nerves of two types of coverings of a sphere $S^{d-1}$: (1) coverings by open hemispheres; (2) antipodal coverings by closed hemispheres. In the first case, nerve theorem implies that the nerve is homotopy equivalent to $S^{d-1}$. In the second case, we prove that the nerve is homotopy equivalent to ...
Added: October 5, 2023
Vlasenko D., Zaikin A., Zakharov D., Известия высших учебных заведений. Прикладная нелинейная динамика 2023 Т. 31 № 5 С. 661–669
Because the brain is an extremely complex hypernet of interacting macroscopic subnetworks, full-scale analysis of brain activity is a daunting task.Nevertheless,this task can be greatly simplified by analysing the correspondence between various patterns of macroscopic brain activity, forex ample,through functional magneticresonance imaging(fMRI) scans, and the performance of particular cognitive tasks or pathological states.The purpose of ...
Added: October 4, 2023
Miasnikof P., Shestopaloff A., Pitsoulis L. et al., Journal of Complex Networks 2022 Vol. 10 No. 1 Article cnac003
In this study, we compare distance measures with respect to their ability to capture vertex community structure and the scalability of their computation. Our goal is to find a distance measure which can be used in an aggregate pairwise minimization clustering scheme. The minimization should lead to subsets of vertices with high induced subgraph density. ...
Added: November 21, 2022
Kiselev D., Makarov I., IEEE Access 2022 Vol. 10 P. 123614–123621
Temporal graph networks are powerful tools for solving the cold-start problem in sequential recommender systems. However, graph models are susceptible to feedback loops and data distribution shifts. The paper proposes a simple yet efficient graph-based exploration method for the mitigation of the issues above. It adopts the counter-based state exploration from reinforcement learning to the ...
Added: September 5, 2022
Korotyaev Evgeny, Saburova N., Mathematische Annalen 2020 Vol. 337 P. 723–758
We consider a Laplacian on periodic discrete graphs. Its spectrum consists of a finite
number of bands. In a class of periodic 1-forms, i.e., functions defined on edges of
the periodic graph, we introduce a subclass of minimal forms with a minimal number
I of edges in their supports on the period. We obtain a specific decomposition of ...
Added: February 5, 2021
Vikentyeva O., Morozenko V. V., Plotnikova E. G. et al., Пермь: ИЦ «Титул», 2020.
Данный учебник и практикум представляет основные разделы дисциплины «Дискретная математика»: множества, комбинаторика, графы. Учебник и практикум содержит необходимый теоретический материал, излагаемый в доступной форме и иллюстрированный большим количеством примеров, а также разнообразные по содержанию и сложности задания для самостоятельного решения.
Учебник и практикум подготовлен на основе многолетнего опыта работы авторов и апробирован на практических занятиях в ...
Added: November 16, 2020
Guterman A., Maksaev A., Acta Scientiarum Mathematicarum 2018 Vol. 84 No. 1-2 P. 19–38
We prove that additive transformations on matrices over the binary Boolean semiring that preserve the scrambling index are automatically bijective. As a consequence we characterize such maps for matrices over an arbitrary antinegative semiring with identity and without zero-divisors. ...
Added: October 30, 2020