Complexity verification through design and analysis of computer experiments
by Niraj Kumar Singh; Soubhik Chakraborty; Dheeresh Kumar Mallick
International Journal of Computational Complexity and Intelligent Algorithms (IJCCIA), Vol. 1, No. 2, 2019

Abstract: This research article is a systematic study towards exploring the parameterised behaviour of smart sort, a comparison based sorting algorithm. Our observation for quick sort led us to conjecture that for sufficiently large samples of fixed size, the average case runtime complexity is: y_avg(n, t_d) = O_emp(t_d), where y_avg denotes the average complexity with parameters n and t_d denoting the input size and frequency of an element (tie density) respectively. The notation O_emp (also called empirical-O) is the statistical bound estimate obtained by running computer experiments. Performance of heap sort is better for discrete inputs with low k values (or equivalently high t_d values) and the runtime reaches to maximum beyond a threshold k. These two observations are opposite in their behaviour. The smart sort, which is designed by combining the key functions of standard quick and heap sort algorithms, is expected to behave optimally with respect to the different input parameters. The robustness of average case O_emp(nlog₂n) complexity for smart sort is conjectured as result of study for various regression models and factorial design experiments.

Online publication date: Tue, 26-Nov-2019

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