Discrete mathematics and its applications (2nd ed.)
Discrete mathematics and its applications (2nd ed.)
Foundations of algorithms using C++ pseudocode (2nd ed.)
Foundations of algorithms using C++ pseudocode (2nd ed.)
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There exists a variety of techniques for the computational complexity analysis of algorithms and functions. This analysis is imperative to the algorithmic and the functional performance. Besides the big-oh complexity, there are other complexity notations, such as Ω, Θ, small o and small ω notational complexities. Complexity analysis is used to select an appropriate algorithm for solving a given problem using computer. Unfortunately, most of the prevailing approaches lack in simplicity and consistency. Existing techniques are complex, and rather difficult to practice in applications. There is a trend to exploit the notational complexities in the existing literature by treating those as functions instead of sets. In this paper, different notational complexities and their paradigms are studied from the new perspectives. Simplified and consistent approaches are introduced that will make the analysis even simpler and easier to follow. Abused notational complexities are analyzed through the appropriate approach.