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2. Perturbation-minimising frequency assignment to address short term demand fluctuation in cellular networkSoumen Atta, Priya Ranjan Sinha Mahapatra, 2018, original scientific article Abstract: In cellular network short term demand fluctuation is a very common phenomenon. The demand of any cell may increase or decrease slightly or the system may expand by adding additional cells or the system may shrink if the demands of certain number of cells become zero. In this paper, the perturbation-minimising frequency assignment problem (PMFAP) is considered to address the short term fluctuation in demand vector. PMFAP is a frequency assignment problem in which newly generated demands are satisfied with minimum changes in the already existing frequency assignment keeping all the interference constraints. In this paper, an efficient heuristic algorithm for PMFAP is presented. The efficiency of this algorithm is compared with the existing results from literature. With a slight modification to the proposed algorithm, it can solve the well-known frequency assignment problem (FAP) and its performance is also compared with the existing results using the standard benchmark data sets for FAP. Keywords: short term demand fluctuation, frequency assignment problem, FAP, PMFAP, cellular network, perturbation, heuristic algorithm Published in RUNG: 17.04.2023; Views: 1798; Downloads: 0 This document has many files! More... |
3. L (D, 2, 1)-labeling of Square GridSoumen Atta, Priya Ranjan Sinha Mahapatra, 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. Keywords: Graph labeling, Square grid, Labeling number, Frequency assignment problem (FAP) Published in RUNG: 17.04.2023; Views: 1416; Downloads: 0 This document has many files! More... |
4. No-hole λ-L (k, k – 1, …, 2,1)-labeling for square gridSoumen Atta, Stanisław Goldstein, Priya Ranjan Sinha Mahapatra, 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. Keywords: graph labeling, labeling number, no-hole labeling, square grid, frequency assignment problem, approximation ratio Published in RUNG: 17.04.2023; Views: 1866; Downloads: 0 This document has many files! More... |