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Least-square fit
Aleksander Đorđević, 2021, research project (high school)

Found in: ključnih besedah
Keywords: least-square fit, non-linear regression, Levenberg-Marquardt algorithm
Published: 28.06.2021; Views: 1462; Downloads: 0
.pdf Fulltext (469,84 KB)

L (D, 2, 1)-labeling of Square Grid
Priya Ranjan Sinha Mahapatra, Soumen Atta, 2019, original scientific article

Abstract: For a fixed integer $D (\geq 3)$ and $\lambda$ $\in$ $\mathbb{Z}^+$, a $\lambda$-$L(D, 2, 1)$-$labeling$ of a graph $G = (V, E)$ is the problem of assigning non-negative integers (known as labels) from the set $\{0, \ldots, \lambda\}$ to the vertices of $G$ such that if any two vertices in $V$ are one, two and three distance apart from each other then the assigned labels to these vertices must have a difference of at least $D$, 2 and 1 respectively. The vertices which are at least $4$ distance apart can receive the same label. The minimum value among all the possible values of $\lambda$ for which there exists a $\lambda$-$L(D, 2, 1)$-$labeling$ is known as the labeling number. In this paper $\lambda$-$L(D, 2 ,1)$-$labeling$ of square grid is considered. The lower bound on the labeling number for square grid is presented and a formula for $\lambda$-$L(D, 2 ,1)$-$labeling$ of square grid is proposed. The correctness proof of the proposed formula is given here. The upper bound of the labeling number obtained from the proposed labeling formula for square grid matches exactly with the lower bound of the labeling number.
Found in: ključnih besedah
Keywords: Graph labeling, Square grid, Labeling number, Frequency assignment problem (FAP)
Published: 17.04.2023; Views: 91; Downloads: 0
.pdf Fulltext (304,64 KB)

No-hole λ-L (k, k – 1, …, 2,1)-labeling for square grid
Priya Ranjan Sinha Mahapatra, Stanisław Goldstein, Soumen Atta, 2017, original scientific article

Abstract: Motivated by a frequency assignment problem, we demonstrate, for a fixed positive integer k, how to label an infinite square grid with a possibly small number of integer labels, ranging from 0 to λ −1, in such a way that labels of adjacent vertices differ by at least k, vertices connected by a path of length two receive values which differ by at least k − 1, and so on. The vertices which are at least k + 1 distance apart may receive the same label. By finding a lower bound for λ, we prove that the solution is close to optimal, with approximation ratio at most 9/8. The labeling presented is a no-hole one, i.e., it uses each of the allowed labels at least once.
Found in: ključnih besedah
Keywords: graph labeling, labeling number, no-hole labeling, square grid, frequency assignment problem, approximation ratio
Published: 17.04.2023; Views: 102; Downloads: 0
.pdf Fulltext (176,29 KB)

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