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Value Engineering of Requirements
Published in Phillip A. Laplante, Mohamad H. Kassab, Requirements Engineering for Software and Systems, 2022
Phillip A. Laplante, Mohamad H. Kassab
On the other hand, algorithmic complexity reflects the complexity of the algorithm used to solve the problem. A key distinction between computational complexity theory and analysis of the algorithm is that the latter is devoted to analyzing the number of resources needed by a particular algorithm to solve a concrete problem, whereas the former asks a more general question. Namely, it targets classifying problems that can, or cannot, be solved with appropriately restricted resources. A mathematical notation called big-O notation is used to define an order relation on functions. The big-O form of a function is derived by finding the dominating term f(n). Big-O notation captures the asymptotic behavior of the function. Using this notation, the efficiency of algorithm A is O(f(n)), where, for input size n, algorithm A required at most O(f(n)) operations in the worst case.
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 computer science, big O notation is used to understand algorithms on how their running time or space requirements grow with increases in input size. It is typically used to provide an upper bound on the growth rate of the function. The big O notation gives us the upper bound idea, which is typically used to represent the time and space complexity of an algorithm. In the following, we formally define the big O notation. Let f(n) and g(n) be two non-negative increasing functions, shown in Fig. 12.1. A function f(n)=O(g(n)) if there are constants, which are c(> 0) and n0 > 0, such that 0 ≤ f(n) ≤ cg(n), for all n ≥ n0.
Mathematical Background
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
Roughly speaking, polynomial-time algorithms can be equated with good or efficient algorithms, while exponential-time algorithms are considered inefficient. There are, however, some practical situations when this distinction is not appropriate. When considering polynomial-time complexity, the degree of the polynomial is significant. For example, even though an algorithm with a running time of O(nln ln n), n being the input size, is asymptotically slower that an algorithm with a running time of O(n100), the former algorithm may be faster in practice for smaller values of n, especially if the constants hidden by the big-O notation are smaller. Furthermore, in cryptography, average-case complexity is more important than worst-case complexity — a necessary condition for an encryption scheme to be considered secure is that the corresponding cryptanalysis problem is difficult on average (or more precisely, almost always difficult), and not just for some isolated cases.
Arrangement and Accomplishment of Interconnected Networks with Virtual Reality
Published in IETE Journal of Research, 2022
This is a project underway that builds the simulated realism transmission standard, particularly to connected VR. This definition of connectivity needs as one of the key difficulties for connected audiovisual and VR affects most of several aforementioned concerns [6]. A systematic method of transmitting consumer demands through to the telecommunication layer is still a work in progress, and mappings across multiple layers of QoS definition “is only becoming to be recognized.” In this study, we offer the interconnectivity paradigm, which reflects an internet perspective of a decentralized VE [7], as a complement to continuing studies. The concept goes into further depth on capacity needs for shareable virtualized entities that vary as a consequence of human activities. In a test case, an experimental multiuser connected VE for remote monitoring of a robot manipulator was employed. This VE uses a mixture of common technologies, including VRML, Distributed Interactive Simulation (DIS), and Java [8–10], to operate across User Datagram Protocol (UDP) employing IP multiplex. A virtual environment is a programme that creates separated python virtual environments for distinct projects to keep their dependencies separate. Most Python programmers utilise this as one of their most significant tools. When assessing an algorithm's efficiency, Big O notation is used to indicate the complexity of the method, which in this context refers to how effectively the algorithm scales with the size of the dataset.
Designing a lightweight 1D convolutional neural network with Bayesian optimization for wheel flat detection using carbody accelerations
Published in International Journal of Rail Transportation, 2021
Dachuan Shi, Yunguang Ye, Marco Gillwald, Markus Hecht
A model for fault diagnosis typically contains signal processing and classification. It should take into account both processes to design a lightweight diagnosis method. The computational time complexity of several common methods for signalling processing and classification is listed in Table 1. The big O notation expresses the asymptotic behaviour of time complexity, where is the size of the inputs. It should be noticed that the computational complexity for classification methods refers to testing complexity, rather than training complexity. It has been commonly thought that machine learning (ML)-based models for classification have very high computational costs. It is true when it refers to training complexity. Once the models are trained and deployed, the trained models have much less computational complexity, being comparable to signal processing, as shown in Table 1. The frequency analysis techniques like FFT, Hilbert transformation, and EMD have even much higher complexity, especially when the input size is large. It is quite challenging to perform such frequency analysis on a low-consumption embedded system. The complexity of LCNN is not listed since it significantly depends on the architecture. A well-designed LCNN could have less complexity than a signal processing method. (This is shown in Section 4.3.) Therefore, the computational costs of both signal processing and classification should be considered. If the signalling processing could be avoided, it will save much computational resource.
Optimal scheduling of vehicle-to-Grid power exchange using particle swarm optimization technique
Published in International Journal of Computers and Applications, 2022
The time complexity of the proposed algorithm is analyzed by changing the input size by means of the number of EVs involved. So, the execution time for different number of EVs (from 100 to 2000 EVs) is evaluated which gives us a relationship between execution time and input size which can be demonstrated graphically as shown in Figure 19. We can observe that the graph is almost linear, which means time would vary linearly with variation in the input size. So the Big O notation for the proposed algorithm is O(n).