• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • The Problem of a Symmetric Graph with a Maximum Number of Vertices and Minimum Diameter
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
October 1, 2026
HSE Researchers Show How Congenital Motor Disorders Affect Brain Development
Researchers from HSE University’s Institute for Cognitive Neuroscience have synthesised the findings of their previous studies on brain development in children with obstetric brachial plexus palsy and arthrogryposis. Their analysis shows that impaired motor function in early childhood not only limits children’s motor experience but also affects memory, categorical thinking, and information processing. The study has been published in Frontiers in Psychology.
October 1, 2026
Window into the Body: Scientists Develop Neural Network to Detect Risk of 15 Diseases from Retinal Images
Russian universities, with the participation of HSE University, Sber, and Z-union, have developed a neural network that can simultaneously assess the risk of 15 types of pathology from retinal photographs, including not only eye diseases but also cardiovascular conditions. The AI system can help clinicians detect potentially concerning changes at an early stage, identify signs reflecting the condition of retinal blood vessels, and determine whether a patient may need further examination. The paper has been published in Frontiers in Medicine.
September 30, 2026
'We Did Not Limit the Time for Questions'
The International Laboratory for Supercomputer Atomistic Modelling and Multi-Scale Analysis at HSE University held a major conference on molecular dynamics. Participants had the opportunity to attend all the presentations, while speakers were given as much time as they needed to answer questions. The HSE News Service interviewed Grigory Smirnov, Head of the Laboratory, and Genri Norman, Chief Research Fellow, about the conference preparations and the discussions it generated.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

The Problem of a Symmetric Graph with a Maximum Number of Vertices and Minimum Diameter

Lobachevskii Journal of Mathematics. 2023. Vol. 44. No. 12. P. 5453–5459.
A. M. Sukhov, A. Y. Romanov, A. A. Amerikanov

The paper gives a solution for the problem of the topology of the communication subsystem graph for high-performance multi-core computing systems. In this graph, each vertex is connected to four neighbors, and the number of vertices is the maximum for a given graph diameter. The solution to this problem is the family of circulants C(D(D+1)+1; 1,  2D+1) , D  – diameter. This graph is invariant under transforming its arbitrary vertex into any other, and its vertices are located densely in the vicinity of the root vertex, which determines its compliance with the diameter optimality criterion. All statements formulated during the solution of the problem are proven.

Research target: Computer Science Mathematics Electronics and Electrical Engineering
Language: English
Full text
DOI
Keywords: computing clusternetwork-on-chipcirculant topologymulti-processor system-on-chip
Similar publications
Инкрементальный метод обновления многомерного куба по неупорядоченному потоку событий журналов информационных систем
Zykov S. V., Уфимцев Г. А., Моделирование, оптимизация и информационные технологии 2026 Т. 14 № 8 С. 1–13
Информационные системы формируют большие объёмы событийных журналов, которые используются для анализа работы приложений и сервисов. При этом события могут поступать в аналитический контур позже момента их фактического возникновения и не в исходном порядке. Такая рассинхронизация приводит к ошибкам при построении агрегированных временных показателей, а регулярный полный пересчёт многомерного аналитического куба требует значительных вычислительных затрат. Целью ...
Added: October 2, 2026
Polarization of opinions in the group: a modeling algorithm considering the dynamics of social bonds
Chebotarev V., Andreyuk D., Elizarova Anastasiya et al., Procedia Computer Science 2022 Vol. 213 No. C P. 596–601
The dynamics of opinion in a group are of interest for a number of practical purposes. In particular, consensus helps and polarization of opinions hinders cohesive teamwork. Existing approaches for modeling opinion dynamics mostly do not take into account the dynamism of social relations in a group. This paper proposes an algorithm and a program ...
Added: October 2, 2026
Enhancing Boundary Stability in Decision Trees and Random Forests: A Weighted Sample Duplication Approach
Konstantinov A., Elizarova Anastasiya P., Utkin L., Computing, Telecommunications and Control 2026 Vol. 19 No. 1 P. 16–25
Decision trees and their ensemble extensions, such as random forests, are widely used as classification models due to their simplicity and interpretability. However, in many real-world tasks where class labels overlap in the feature space, standard decision trees rely on hard splits that create fragile decision boundaries. In these regions, small perturbations in the input ...
Added: October 2, 2026
Graphon spin systems as exactly solvable models
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Планетарное зацепление трилистника
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Bayesian Adaptive Sparse Copula
Prokhorov A., Burda M., Journal of Computational and Graphical Statistics 2026 P. 1–13
Bayesian nonparametric density estimation procedures are typically based on single-scale priors, such as Dirichlet process mixtures. Alternative multiscale density priors built on decision trees have many well-known advantages, including the ability to characterize abrupt local changes and to provide an estimate with a desired level of resolution. Despite their theoretical appeal, multiscale methods have typically ...
Added: October 2, 2026
Pericyte-derived cancer-associated fibroblasts correlate with poor survival and are enriched after chemoradiotherapy in glioblastoma
Aly Ismailov, Poptsova M., Plos One 2026 Vol. 21 No. 9 Article e0355902
Added: October 2, 2026
A quantum–analogue formalism for modeling supraliminal information processing
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Консервативные энтропийно и энергетически корректные разностные методы для одномерных квазигазодинамических систем уравнений
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству  консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
On some arithmetic conditions of recurrent sequences modulo prime p
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Fractional Macroscopic Fluctuation Theory for a Superdiffusive Ginzburg-Landau dynamics
Bernardin C., João P. M., Gonçalves P., PROBABILITY AND MATHEMATICAL PHYSICS 2026 P. 59–59
We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the corresponding stationary profile is characterized by a fractional Laplace equation. We establish a dynamical large deviations principle for the empirical measure and derive the associated stationary ...
Added: October 1, 2026
Long-time behaviour of dynamical systems driven by bounded mixing noises
Kuksin S., Dynamical Systems 2026
We study the mixing properties of discrete-time and continuous-time dissipative dynamical systems driven by bounded mixing random forces. The continuous-time systems are reduced to discrete-time random dynamical systems generated by time-one maps, so that the main analysis is carried out in the discrete setting. We introduce a class of mixing random forcings whose regular conditional distributions with ...
Added: October 1, 2026
Markovian reduction and exponential mixing in total variation for random dynamical systems
Kuksin S., Shirikyan A., Journal of Dynamics and Differential Equations 2026 P. 1098–1100
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure ...
Added: October 1, 2026
Bounds on the derivatives of the log-cumulative distribution function of the multivariate normal distribution
Potanin B., Dolgikh S., Statistics and Probability Letters 2027 Article 110984
We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...
Added: October 1, 2026
Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence (IJCAI 2026)
International Joint Conferences on Artificial Intelligence, 2026.
Added: October 1, 2026
Asymptotics of Spectrum and Quantum Averages of the Hydrogen Atom in a Magnetic Field Near the Upper Boundaries of Spectral Clusters
A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545
We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using irreducible representations of the Karasev–Novikova algebra with quadratic commutation relations. We find the asymptotics of a series of eigenvalues and the corresponding asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...
Added: October 1, 2026
Ensemble-based Prototype-Augmented Multimodal Fusion for Ambivalence/Hesitancy Recognition
Ryumina E., Aksenov A., Сысоев Д. С. et al., IEEE Computer Society, 2026.
Ambivalence/hesitancy recognition in unconstrained videos is a challenging problem due to the subtle, multimodal, and context-dependent nature of this behavioral state. In this paper, a multimodal approach for video-level ambivalence/hesitancy recognition is presented for the 10th ABAW Competition. The proposed approach integrates four complementary modalities: scene, face, audio, and text. Scene dynamics are captured with ...
Added: September 30, 2026
Simultaneous approximation of the score function and its derivatives by deep neural networks
Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...
Added: September 30, 2026
Traffic Patterns in Networks-on-Chip: A Survey
Malikov M., Romanov A., IEEE Access 2025 Vol. 13 P. 148803–148815
Networks-on-chip (NoCs) widespread in computing system design are used in many applications. A critical NoC aspect is the interaction between computing cores and in particular the traffic patterns. The relevance of this work stems from the fact that traffic patterns in NoCs are poorly understood and have no general classification; and there are no universal ...
Added: September 16, 2025
Cycle-accurate multi-FPGA platform for accelerated emulation of large on-chip networks
Romanov A., Lerner A., Amerikanov A., The Journal of Supercomputing 2024 No. 80 P. 22462–22478
On-chip networks (NoCs) have become a popular choice for designing large multiprocessor architectures. Software-based emulation is often used to perform the design verifcation. However, if the considered design is sufciently large, softwarebased emulation becomes impractically slow. To avoid this limitation, multi-FPGA emulation was introduced, where multiple interconnected FPGAs collectively emulate a single circuit. The number ...
Added: June 30, 2024
Implementation of Regular Topologies for NoCs Based on schoolMIPS Soft-Processor Cores
Mikhail Yu. Romashikhin, , in: Proceedings 2024 International Russian Smart Industry Conference (SmartIndustryCon), 25-29 March 2024.: Sochi: IEEE, 2024. P. 104–108.
This article describes the implementation of regular topologies for networks-on-chip. The complexity of network development and its main parameters depend on the choice of topology. The rationale for the influence of topology on network bandwidth is given. Software that automates the generation of configuration files (bitstream) for the implementation of networks-on-chip with different topologies and ...
Added: May 13, 2024
Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip
Sukhov A., Romanov A., Selin M., Symmetry 2024 Vol. 16 No. 1 Article 127
In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest routes between the two nodes based on coordinates are formulated. A technique ...
Added: March 8, 2024
Маршрутизация в циркулянтных графах на основе виртуальной координатной системы
Sukhov A., Romanov A., Глушак Е. В., Ученые записки Казанского университета. Серия: Физико-математические науки 2023 Т. 165 № 3 С. 282–293
The article discusses routing methods in two-dimensional circulant graphs (each vertex is connected to four neighboring ones). The unique group of symmetries of the circulant graph makes it possible to use it as a topology for high performance computing devices, including networks-on-chip and cluster supercomputers. It is shown that the minimum number of transitions along ...
Added: January 5, 2024
The Dataset for Optimal Circulant Topologies
Romanov A., Big Data and Cognitive Computing 2023 Vol. 7 No. 2 Article 80
This article presents software for the synthesis of circulant graphs and the dataset obtained. An algorithm and new methods, which increase the speed of finding optimal circulant topologies, are proposed. The results obtained confirm an increase in performance and a decrease in memory consumption compared to the previous implementation of the circulant topologies synthesis method. ...
Added: June 4, 2023
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit