The present paper makes use of factorial experiments to assess software complexity using insertion sort as a trivial example. We next propose to implement the methodology in quicksort and other advanced algorithms.

Quicksort is one of the earliest and most famous algorithms. It was invented and analyzed by Tony Hoare around 1960. This was before the big-O notation was used to analyze algorithms. Hoare invented the algorithm while an exchange student at Moscow State University while studying probability under Kolmogorov—one of the most famous researchers in probability theory. The analysis we will cover is...

Average case analysis forms an interesting and intriguing part of algorithm theory since it explains why some algorithms with bad worst-case complexity can better themselves in performance on the average. Well known examples include the quicksort, simplex method and the wide variety of computer graphics and computational geometry algorithms. Here we make a statistical case study of the robustne...

Quicksort can be made to go quadratic by constructing input on the fly in response to the sequence of items compared. The technique is illustrated by a specific adversary for the standard C qsort function. The general method works against any implementation of quicksort–even a randomizing one–that satisfies certain very mild and realistic assumptions. When using quicksort one often feels a nagg...

In this paper, we propose a useful replacement for quicksort-style utility functions. The replacement is called Symmetry Partition Sort, which has essentially the same principle as Proportion Extend Sort. The maximal difference between them is that the new algorithm always places already partially sorted inputs (used as a basis for the proportional extension) on both ends when entering the part...

The contraction method for recursive algorithms is extended to the multivariate analysis of vectors of parameters of recursive structures and algorithms. We prove a general multivariate limit law which also leads to an approach to asymptotic covariances and correlations of the parameters. As an application the asymptotic correlations and a bivariate limit law for the number of key comparisons a...

In this master thesis we analyze the complexity of sorting a set of strings. It was shown that the complexity of sorting strings can be naturally expressed in terms of the prefix trie induced by the set of strings. The model of computation takes into account symbol comparisons and not just comparisons between the strings. The analysis of upper and lower bounds for some classical algorithms such...

Algorithm performance coverage in textbooks emphasizes patterns of growth in execution times, relative to the size of the problem. Variability in execution times for a given problem size is usually ignored. In this research study, our primary focus is on the empirical distribution of execution times for a given algorithm and problem size. We examine CPU times for Java implementations of five so...