Document Type
Article
Abstract
A Theory of sorting is developed in which each sorting algorithm is viewed as a sequence of comparisons accumulating ordering constraints into a hierarchical structure which reflects both element partitions and partial ordering information in the form of directed acyclic graphs. Each such structure, called a HIPPO, has a well-defined order ambiguity which is a measure of how much work remains to determine the exact order of elements. The theory is used to analyze 20 algorithms from Knuth's definitive volume (l] with some startling results and a somewhat novel taxonomy is suggested based on the HIPPO paradigm. HIPPO theory and order ambiguity easily and naturally incorporate concerns for correctness and termination of sorting algorithms. An efficiency measure based on order ambiguity reflects how well a method is progressing. Several theoretical results.are proved for efficiency and empirical data are tabulated to provide better intuitive understanding of various methods.
Recommended Citation
Zahn, Charles T., "A Comparison-Based Theory for the Analysis of Sorting Algorithms" (1986). CSIS Technical Reports. 143.
https://digitalcommons.pace.edu/csis_tech_reports/143
Comments
This document was officially published as a Technical Report for the CSIS (Computer Science and Information Systems) Department of Pace University, September 1986.