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Journal ArticleDOI

Some Theorems on Sorting

Robert Morris
- 01 Jan 1969 - 
- Vol. 17, Iss: 1, pp 1-6
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TLDR
A somewhat better lower bound for the average number of comparisons required to sort a table of N items is $\log _2 N!$, where the average is taken over all possible permutations of the table.
Abstract
It is a “well-known fact” that a lower bound for the average number of comparisons required to sort a table of N items is $\log _2 N!$, where the average is taken over all possible permutations of the table. In this paper a somewhat better lower bound is obtained, which in a way provides considerable insight into the theoretical limitations on methods of sorting by comparison.

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Journal ArticleDOI

Static scheduling algorithms for allocating directed task graphs to multiprocessors

TL;DR: A taxonomy that classifies 27 scheduling algorithms and their functionalities into different categories is proposed, with each algorithm explained through an easy-to-understand description followed by an illustrative example to demonstrate its operation.
Journal ArticleDOI

Implementing Quicksort programs

TL;DR: A detailed implementation combining the most effective improvements to Quicksort is given, along with a discussion of how to implement it in assembly language, including how to apply various code optimization techniques.
Journal ArticleDOI

Samplesort: A Sampling Approach to Minimal Storage Tree Sorting

TL;DR: A procedure is proposed which is a generalization of minimal storage tree sorting and which has the following three properties: there is a significant improvement in the expected number of comparisons required to sort the input sequence, the procedure is statistically insensitive to bias in theinput sequence, and the expected numbers of comparisons approaches the information-theoretic lower bound on the number of compared required.
Journal ArticleDOI

The analysis of Quicksort programs

TL;DR: Results are derived which make it possible to obtain exact formulas describing the total expected running time of particular implementations on real computers of Quicksort and an improvement called the median-of-three modification.
Journal ArticleDOI

Cophenetic metrics for phylogenetic trees, after Sokal and Rohlf

TL;DR: In this paper, the authors define a family of cophenetic metrics dφ,p for weighted phylogenetic trees with nested taxa, which can be computed in O(n 2 ) time, where n is the number of taxa.