Mixed hourglass graph

2023

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Quadrant Interlocking Factorization (QIF), an alternative to LU factorization, is suitable for factorizing invertible matrix A such that det(A) , 0. The QIF, with its application in parallel computing, is the most efficient matrix factorization technique yet underutilized. The two forms of QIF among others, which are not only similar in algorithm but also in computation, are WZ factorization and WH factorization yet differs in applications and properties. This review discusses both the old form of QIF, called WZ factorization, and the latest form of QIF, called WH factorization, with an example and open questions to further the studies between the two factorization techniques.

Section: Application Of W H Factorization and Hourglass Matrixmentioning

confidence: 99%

Section: Application Of W H Factorization and Hourglass Matrixmentioning

confidence: 99%

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A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

Bashir

Kamarulhaili

2023

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“…A weighted graph or edge-labeled graph has edges (directed or undirected) having a non-negative value called weight. An unweighted graph can be considered a weighted graph if each of the edges has a numerical value of weight 1 [16]. The number of vertices (nodes or points) in G, written as v(G), is the order of a graph while the number of edges in graph G, written as e(G), is the size of a graph [17].…”

Section: Graphs Classificationmentioning

confidence: 99%

Graph Theory: A Lost Component For Development in Nigeria

2022

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Graph theory is one of the neglected branches of mathematics in Nigeria but with the most applications in other fields of research. This article shows the paucity, importance, and necessity of graph theory in the development of Nigeria. The adjacency matrix and dual graph of the Nigeria map were presented. The graph spectrum and energies (graph energy and Laplacian energy) of the dual graph were computed. Then the chromatic number, maximum degree, minimum spanning tree, graph radius, and diameter, the Eulerian circuit and Hamiltonian paths from the dual graph were obtained and discussed.

“…Babarinsa and Kamarulhaili [18] gave details on hourglass matrix and its factorization algorithm by restricting the computed entries of the factorization to be nonzero in comparison with an hourglass device. They also suggested its applications in mathematics, graph theory, statistics, and computer science, see [19][20][21][22][23][24]. An hourglass matrix is defined as a nonsingular matrix of order n (n ≥ 3) with nonzero entries from the ith to the (n − i + 1) element of the ith and (n − i + 1) row of the matrix, 0's otherwise for i = 1, 2, ..., n+1 2 [18].…”

Section: Hourglass Matrixmentioning

confidence: 99%

Application of hourglass matrix in Goldreich-Goldwasser-Halevi encryption scheme

Ihinkalu

Cyril-Okeme

et al. 2022

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Goldreich-Goldwasser-Halevi (GGH) encryption scheme is lattice-based cryptography with its security based on the shortest vector problem (SVP) and closest vector problem (CVP) with immunity to almost all attacks, including Shor's quantum algorithm and Nguyen's attack of higher lattice dimension. To improve the efficiency and security of the GGH Scheme by reducing the size of the public basis to be transmitted, we use an hourglass matrix obtained from quadrant interlocking factorization as a public key. The technique of quadrant interlocking factorization to yield a nonsingular hourglass matrix compensates the encryption scheme with better efficiency and security.