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Optimal Two-Sided Embeddings of Complete Binary Trees in Rectangular Grids
Computational Mathematics and Modeling. 2019. Vol. 30. No. 2. P. 115–128.
Высоцкий Л. И., Ложкин С. А.
The article considers the construction of optimal-area homeomorphic embeddings of complete binary trees in rectangular grids such that the leaf images are on the opposite sides of the grid and the edge images intersect only at node images. The minimum grid area that admits the embedding of a complete binary tree of depth n is shown to be asymptotically equal to n/3 2^n. An algorithm to construct an asymptotically optimal embedding of such a tree is proposed; the complexity of the algorithm is O(n2^n) bit operations.
Shabanov N., Kuricheva O., Kurbatova J. et al., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.
The carbon balance of an ecosystem is the difference between Gross Primary Productivity (GPP) and Ecosystem Respiration (Reco) as expressed by Net Ecosystem Exchange (NEE). While remote sensing retrievals of GPP have reached maturity, Reco estimation remains underexplored and ultimately cast bias on NEE. Here we present an end-to-end multi-scale analysis of the mechanism of ...
Added: August 21, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Petrovanov I., Sergeev A., / Series Computer Science "arxiv.org". 2025. No. 2512.18332.
Transport coding reduces message delay in packet-switched networks by introducing controlled redundancy at the transport layer: original packets are encoded into coded packets, and the message is reconstructed after the first successful deliveries, effectively shifting latency from the maximum packet delay to the -th order statistic. We present a concise, reproducible discrete-event implementation of transport coding in OMNeT++, including ...
Added: December 24, 2025
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Anton Begehr, Peter Panfilov, , in: ICCTA '22: Proceedings of the 2022 8th International Conference on Computer Technology Applications.: NY: Association for Computing Machinery (ACM), 2022. Ch. 19 P. 121–127.
In this work, we explore the application of graph embedding to the design and development of a friend recommender system for the users of the social network. Graph embedding could be useful for recommendation tasks because of data compression, the feature vector format, and sub-quadratic time complexity of graph embedding. We suggest and study a ...
Added: September 26, 2022
Karpov I., Roman Marakulin, , in: Data Analytics and Management in Data Intensive Domains. 23rd International Conference, DAMDID/RCDL 2021, Moscow, Russia, October 26–29, 2021, Revised Selected Papers.: Springer, 2022. P. 36–50.
With the rise of the competition in the movie production market, because of new players such as Netflix, Hulu, HBO Max, and Amazon Prime, whose primary goal is producing a large amount of exclusive content in order to gain a competitive advantage, it is extremely important to minimize the number of unsuccessful titles. This paper ...
Added: September 4, 2021
Karpov I., Glazkova E., , in: Recent Trends in Analysis of Images, Social Networks and Texts. 9th International Conference, AIST 2020, Skolkovo, Moscow, Russia, October 15–16, 2020 Revised Supplementary ProceedingsVol. 12602.: Springer, 2021. P. 11–21.
The widespread of Online Social Networks and the opportunity to commercialize popular accounts have attracted a large number of automated programs, known as artificial accounts. This paper (Project repository available at http://github.com/karpovilia/botdetection) focuses on the classification of human and fake accounts on the social network, by employing several graph neural networks, to efficiently encode attributes and ...
Added: June 19, 2021
Makarov I., Makarov M., Kiselev D., PeerJ Computer Science 2021 Vol. 7 Article e526
Today, increased attention is drawn towards network representation learning, a technique that maps nodes of a network into vectors of a low-dimensional embedding space. A network embedding constructed this way aims to preserve nodes similarity and other specific network properties. Embedding vectors can later be used for downstream machine learning problems, such as node classification, ...
Added: March 31, 2021
Giselsson P., Rantzer A., Springer, 2018.
This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a ...
Added: October 29, 2020
Makarov I., Kiselev D., Nikitinsky N. et al., PeerJ Computer Science 2021 Vol. 7 P. 1–62
Dealing with relational data always required significant computational resources, domain expertise and task-dependent feature engineering in order to incorporate structural information into predictive model. Nowadays, a family of automated graph feature engineering techniques have been proposed in different streams of literature. So-called graph embeddings provide a powerful tool to construct vectorized feature spaces for graphs ...
Added: October 27, 2020
Ananyeva M., Makarov I., Pendiukhov M., , in: Network Algorithms, Data Mining, and Applications. Springer Proceedings in Mathematics & Statistics.: Springer, 2020. P. 85–99.
In this paper, we study the problem of learning graph embeddings for dynamic networks and the ability to generalize to unseen nodes called inductive learning. Firstly, we overview the state-of-the-art methods and techniques for constructing graph embeddings and learning algorithms for both transductive and inductive approaches. Secondly, we propose an improved GSM based on GraphSAGE ...
Added: February 27, 2020
Durandin O., Malafeev A., , in: Analysis of Images, Social Networks and Texts. 8th International Conference, AIST 2019, Kazan, Russia, July 17–19, 2019, Revised Selected Papers. Communications in Computer and Information ScienceVol. 1086.: Springer, 2020. P. 120–131.
In recent works on learning representations for graph structures, methods have been proposed both for the representation of nodes and edges for large graphs, and for representation of graphs as a whole. This paper considers the popular graph2vec approach, which shows quite good results for ordinary graphs. In the field of natural language processing, however, ...
Added: November 16, 2019
Beaudou L., Brewster R., Discrete Mathematics and Theoretical Computer Science 2019 Vol. 21 No. 3 P. 1–13
In 2001, Erwin introduced broadcast domination in graphs. It is a variant of classical domination where selected vertices may have different domination powers. The minimum cost of a dominating broadcast in a graph G is denoted γb(G). The dual of this problem is called multipacking: a multipacking is a set M of vertices such that ...
Added: June 7, 2019
Logachev D., Aleksey Zobnin, / Series math "arxiv.org". 2016.
We continue study of varieties started in a paper of A. Grishkov, D. Logachev "Resultantal varieties related to zeroes of L-functions of Carlitz modules". We give a (conjecturally) complete description of these varieties in terms of rooted binary trees, we find parametrizations of their irreducible components and their invariants: degrees, multiplicities, Jordan forms, Galois actions. ...
Added: November 26, 2017
Osokin A., Vetrov D., Kolmogorov V., , in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2011).: Colorado Springs: IEEE, 2011. P. 1889–1896.
In this paper we address the problem of finding the most probable state of discrete Markov random field (MRF) with associative pairwise terms. Although of practical importance, this problem is known to be NP-hard in general. We propose a new type of MRF decomposition, submodular decomposition (SMD). Unlike existing decomposition approaches SMD decomposes the initial ...
Added: October 18, 2017