Journal ArticleDOI
Some Theorems on Sorting
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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.read more
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Journal ArticleDOI
Static scheduling algorithms for allocating directed task graphs to multiprocessors
Yu-Kwong Kwok,Ishfaq Ahmad +1 more
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
W. D. Frazer,A. C. McKellar +1 more
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.