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Computational Complexity Analysis for Problems in Elastic Optical Networks
Published in Bijoy Chand Chatterjee, Eiji Oki, Elastic Optical Networks: Fundamentals, Design, Control, and Management, 2020
Bijoy Chand Chatterjee, Eiji Oki
In the following, we classify algorithms from the best-to-worst performance in terms of big O notation. A logarithmic algorithm—O(logn); runtime grows logarithmically in proportion to n. A linear algorithm—O(n); runtime grows directly in proportion to n. A superlinear algorithm—O(nlogn); runtime grows in proportion to n. A polynomial algorithm—O(nc); runtime grows quicker than previous all based on n. An exponential algorithm—O(cn); runtime grows even faster than a polynomial algorithm based on n. A factorial algorithm—O(n!); runtime grows the fastest and becomes quickly unusable for even small values of n. Some of the examples of all those types of algorithms are mentioned as follows. Logarithmic algorithm—O(logn)—binary search. Linear algorithm—O(n)—linear search. Superlinear algorithm—O(nlogn)—heap sort and merge sort. Polynomial algorithm—O(nc)—strassen’s matrix multiplication, bubble sort, selection sort, insertion sort, and bucket sort. Exponential algorithm—O(cn)—tower of Hanoi. Factorial algorithm—O(n!)—determinant expansion by minors, and brute force search algorithm for the traveling salesman problem.
Hashing Schemes
Published in Weidong Wu, Packet Forwarding Technologies, 2007
To reduce the complexity of Linear Search, O(W), Waldvogel et al. used the binary search on the array T to cut down the complexity to O(log W). However, for a binary search to make its branching decision, it requires the result of an ordered comparison, returning whether the probed entry is less than, equal, or greater than our search key. If the probed entry is equal to the search key, the match is found. If the probed entry is less than or greater than our search key, we cannot be sure that the search should proceed in the direction of shorter lengths, because the longest-matching prefix could be in the direction of longer length as well. Waldvogel et al. insert extra prefixes of adequate length, called marker, to be sure that, when no match is found, the search must proceed necessarily in the direction of shorter prefixes.
Recent trends and development in hybrid microgrid: a review on energy resource planning and control
Published in International Journal of Sustainable Energy, 2022
Amar Kumar Barik, Smriti Jaiswal, Dulal Chandra Das
A few hybrid optimisation techniques have recently been demonstrated to boost the efficiency of simple algorithms such as Saha and Mukherjee (2018), a quasi-oppositional chaotic antlion optimisation technique that hybridises quasi-counter-based investigation as well as chaotic linear search (CLS) via antlion optimisation technique, Shankar and Mukherjee (2016) proposed Quasi-oppositional harmony search algorithm by hybridising Harmony search algorithm with Quasi-opposition based learning (QOBL) for LFC analysis. Those inspires to hybridise SHO in hµG applications. Sahoo, Routray, and Rout (2020) discussed the microgrid control hierarchy in three segments as primary, secondary, and tertiary strategies for AC/DC/hµGs structures indicating the highpoints of state-of-art control methods such as intelligent control, synchronised and evolutionary approach of hµGs with specific benefits and demerits.
Analysis of a Novel Three-phase Asynchronous Generator Based on Graph Theory for Supplying Single-Phase Load
Published in IETE Journal of Research, 2021
Sambaran Ray, Himadri S. Chatterjee, Sankar N. Mahato, Nirmal K. Roy
Different types of arrangements of three-phase SAG (star and delta) with excitation capacitors have been recommended by many researchers for single-phase operation [25–29]. The steady-state behavior of a star-connected three-phase induction generator with balanced and unbalanced capacitor bank was reported by Fukami et al. [28]. The single-phase load was connected across one of the lines and the neutral point of the star-connected capacitor bank. General analysis of the three-phase SAG under unbalanced conditions, including single-phase load, was presented by Murthy et al. [29]. The symmetrical component theory was applied for deriving two non-linear equations with two unknown variables, namely, per unit magnetizing reactance (Xm) and frequency (a) under certain operating condition in [28,29]. To solve these non-linear equations for “Xm” and “a”, different methods have been used, such as Newton–Raphson [21,22], mathcad personal [28], pattern search method of Hooke and Jeeves [30], Rosenbrock’s gradient method [31], genetic algorithm [32], particle swarm optimization (PSO) [33], linear search algorithm (LSA) and binary search algorithm (BSA) [34]. Also, the voltage and frequency regulation schemes of SAG have been reported in [35–38].
Transients in flexible manufacturing systems with setups and batch operations: Modeling, analysis, and design
Published in IISE Transactions, 2021
Mengyue Wang, Hongxuan Huang, Jingshan Li
To reduce setups and their associated production interruptions, batch production is often implemented, in which the same type of parts are often grouped into batches. To optimize batch sizes, the economic order quantity model has been used to minimize setup costs in Jamal et al. (2004) and Cárdenas-Barrón (2008). A stochastic dynamic programming model is presented by Bouslah et al. (2013) to minimize the total expected cost of inventory, backlog, and transportation in production planning. With setup costs and mean flow time being selected as the primary and the secondary minimization objectives, respectively, Quadt and Kuhn (2007) consider batch size, time scheduling and machine assignment through genetic algorithms. Using queueing models, Koo et al. (2007) provide a linear search algorithm to find the optimal throughput rate and batch size simultaneously, whereas Meng and Heragu (2004) analyze the effects of batch size on the parametric decomposition procedure.