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Introduction to Algorithms and Data Structures
Published in Sriraman Sridharan, R. Balakrishnan, Foundations of Discrete Mathematics with Algorithms and Programming, 2019
Sriraman Sridharan, R. Balakrishnan
The worst case complexity is the maximum time needed, among all possible inputs of size n, to solve the problem. Stated differently, the worst case tells us the slowest an algorithm can run on an input of size n. In symbol, if TA(n) $ T_A(n) $ is the maximum time taken to solve a problem π $ \pi $ of size n using algorithm A, then TA(n)=max{T(In)|In∈πn} $$ T_A(n) = \max \{\, T(I_n) | I_n \in \pi _n \,\} $$
High-Level Modeling and Design Techniques
Published in Soumya Pandit, Chittaranjan Mandal, Amit Patra, Nano-Scale CMOS Analog Circuits, 2018
Soumya Pandit, Chittaranjan Mandal, Amit Patra
The time complexity of an algorithm is calculated on the basis of the number of required elementary computational steps taken by the algorithm to compute the function it was developed for. The number of steps are interpreted as a function of the input size. However, it may be noted that most of the time, the total number of elementary computational steps varies from input to input because of the presence of conditional statements such as an if-else statement. Therefore, average-case complexity is considered to be a more meaningful characterization of the algorithm. However, accurate determination of the average-case complexity of an algorithm is not an easy task, which necessitates the use of the worst-case complexity metric. The worst-case complexity of an algorithm is the complexity with respect to the worst possible inputs, which gives an upper bound on the average-case complexity.
A unified pedestrian routing model for graph-based wayfinding built on cognitive principles
Published in Transportmetrica A: Transport Science, 2018
Peter M. Kielar, Daniel H. Biedermann, Angelika Kneidl, André Borrmann
The worst-case algorithmic complexity of the simulation method is an important aspect in identifying the practical usability of the concept. Based on the worst-case algorithmic complexities of the individual methods (see Sections 3.1 and 3.2), we can derivate the overall worst-case complexity of the algorithm for a single pedestrian. In the worst case, V vertices have to be visited by a pedestrian to navigate from origin to the destination. At each visited vertex , all of the individual methods are computed. Thus, the worst-case complexity is , with K being the sum of the individual method complexity , which leads to .
Computation of the target state and feedback controls for time optimal consensus in multi-agent systems
Published in International Journal of Control, 2018
Ameer K. Mulla, Deepak U. Patil, Debraj Chakraborty
Computation of and for a triplet {ai, aj, ak} is independent of the computation related to any other triplets. For N-agent system, there are such triplets. As worst case complexity for each triplet is fixed, the run time complexity of computing and is O(N3). Since the computations of and can be performed separately for each triplet and the communication graph is complete, each agent can perform the required computation for such triplets. In general, need not be an integer, and hence after distribution each agent has to perform computations for at most triplets, i.e. O(N2) operations. A heuristic to distribute these computations among the agents is proposed in the Appendix.
Optimal sensor spacing in IoT network based on quantum computing technology
Published in International Journal of Parallel, Emergent and Distributed Systems, 2023
Gopal Krishna, Anish Kumar Saha
The computational complexity indicates the number of computations required to complete the algorithm’s execution. This computation must be low compared to the other algorithms to achieve higher network performance. The Big O notation is one familiar metric for determining an optimisation algorithm’s computational complexity. This notation is generally utilised to define the worst-case scenario of an algorithm that is determined based on the overall execution time required or the memory space utilised by the considered algorithm. The ROA is considered in the proposed work for identifying the optimal sensors in the network. At the initialisation phase, the algorithm consumes a time of where, indicating the total number of iterations and the dimension coordinates. The computation of success rate is one of the important criteria followed in the ROA algorithm. The complexity involved in the computation of the success rate can be indicated as for every rider in the population. Then, the identification of the leading rider in the popular is a complex step, and the computational complexity involved can be indicated in the notation as where indicates the entire iterations carried out to complete the process of sensor selection and indicates the total population in the group. Thus, the worst-case complexity of the algorithm can be indicated as .