Algorithm of Multidimensional Data Transmission Using
Extremal Uniform Hypergraphs

Егорова, Е. К.; Mokryakov, A. V.; Suvorova, A. A.; Цурков, В. И.

doi:10.1134/s1064230721010056

Cited by 4 publications

(6 citation statements)

References 8 publications

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“…We have obtained an elegant and more efficient algorithm for finding the power of the set EUH 3 n . This problem makes not only theoretical but also practical sense if we remember that this parameter is taken into account when used as a key in the topological encryption algorithm [14].…”

Section: Discussionmentioning

confidence: 99%

“…The constructed theory, as is now well seen, has a wide field of practical applications. Let us note only some of them: computer network modeling and design [3,4], including wireless nets [5]; the modeling of transport networks and calculation of loads on them [6]; social interaction analysis [7] and filtering music tracks [8,9]; database design [10] and neural network design [11][12][13]; cryptography [14][15][16][17]; and data visualization [18]. At the same time, hypergraphs themselves are rather amorphous structures, which led to the necessity to distinguish between various classes of hypergraphs with essentially different parameters and constraints: hypertrees [19], hypernetworks [6], and uniform hypergraphs [20][21][22][23][24][25] (also known as complexes [26]).…”

Section: Introductionmentioning

confidence: 99%

“…In works [14][15][16][17], the possibility of using extreme uniform hypergraphs as a key element for a new method of data encryption is presented. This method is topological; the higher the order of uniformity of the hypergraph, the larger the key space at the same number of vertices involved.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

Egorova,

Leonov,

Mokryakov

et al. 2024

Axioms

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This paper continues the study of second-order signature properties—the characterization of the extreme 3-uniform hypergraph. Previously, bases were used to count extreme 3-uniform hypergraphs. However, the algorithm using this mechanism is extremely labor-intensive. The structure of the signature allows us to use it as a more efficient basis for the same problem. Here, we establish the nature of the mutual correspondence between the kind of second-order signature and extreme hypergraphs, and we present a new algorithm to find the power of the set of extreme 3-uniform hypergraphs through the set of their characteristic-signatures. New results obtained with the proposed tool are also presented.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

Egorova,

Leonov,

Mokryakov

et al. 2024

Axioms

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show abstract

“…In fact, researchers can use hypergraphs to describe any model where there are at least some relations between objects. Moreover, unlike graphs, it is possible to describe very complex relationships between groups of objects simultaneously [9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…The latter is true only for the two-dimensional and three-dimensional cases. The obtained characterizations have applications in new algorithms of data encryption [10,12,16], and also help in studies of the class of extreme hypergraphs [23] itself.…”

Section: Introductionmentioning

confidence: 99%

The Algebra of Signatures for Extreme Two-Uniform Hypergraphs

Egorova,

Mokryakov,

Tsurkov

2023

Axioms

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In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal two-uniform hypergraph itself. However, for the signature, although various algorithms have been derived for transforming it into other object-characteristics such as the base, the adjacency matrix, and the vector of vertex degrees, no isolated signature union and intersection apparatus has been constructed. This allows us to build efficient algorithms based on signatures, the most compact representation of extremal two-uniform hypergraphs. The nature of the algebraic construction that can be built on a set of signatures using union and intersection operations has also been defined. It is proved that an algebra on a set of signatures with either the union or intersection operation forms a monoid; if the algebra is defined on a set of signatures with both union and intersection operations, it forms a distributive lattice.

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First and Second Order Signatures of Extreme Uniform Hypergraphs and Their Relationship with Vectors of the Vertex Degrees

Goltsova,

Egorova,

Leonov

et al. 2023

J. Comput. Syst. Sci. Int.

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Algorithm of Multidimensional Data Transmission Using Extremal Uniform Hypergraphs

Cited by 4 publications

References 8 publications

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

Finding Set Extreme 3-Uniform Hypergraphs Cardinality through Second-Order Signatures

The Algebra of Signatures for Extreme Two-Uniform Hypergraphs

First and Second Order Signatures of Extreme Uniform Hypergraphs and Their Relationship with Vectors of the Vertex Degrees

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