Title: A statistical peek into average case complexity

Authors: Niraj K. Singh; Soubhik Chakraborty; Dheeresh K. Mallick

Addresses: Department of Computer Science and Engineering, Birla Institute of Technology, Mesra, 835215, India ' Department of Applied Mathematics, Birla Institute of Technology, Mesra, 835215, India ' Department of Computer Science and Engineering, Birla Institute of Technology, Mesra, 835215, India

Abstract: The present paper gives a statistical adventure towards exploring the average case complexity behaviour of computer algorithms. Rather than following the traditional count-based analytical approach, we instead talk in terms of the weight-based analysis that permits mixing of distinct operations into a conceptual bound called the statistical bound and its empirical estimate, the so called 'empirical O'. Based on careful analysis of the results obtained, we have introduced two new conjectures in the domain of algorithmic analysis. The analytical way of average case analysis falls flat when it comes to a data model for which the expectation does not exist (e.g., Cauchy distribution for continuous input data and certain discrete distribution inputs as those studied in the paper). The empirical side of our approach, with a thrust in computer experiments and applied statistics in its paradigm, lends a helping hand by complimenting and supplementing its theoretical counterpart.

Keywords: average case analysis; mathematical bounds; statistical bounds; big-oh; empirical-O; pseudo linear complexity; tie density; computer algorithms; average case complexity.

DOI: 10.1504/IJEDPO.2014.066470

International Journal of Experimental Design and Process Optimisation, 2014 Vol.4 No.2, pp.116 - 142

Received: 15 Feb 2014
Accepted: 06 Sep 2014

Published online: 21 Dec 2014 *

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