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EnglishThe classification problem transforms a set of N numbers in such a way that none of the first N/2 numbers exceeds any of the last N/2 numbers. A comparator network that solves the classification problem on a set of r numbers is commonly called an r-classifier. This paper shows how the well-known Leighton’s Columnsort algorithm can be modified to solve the classification problem of N = rs numbers using an r-classifier instead of an r-sorting network. Overall, the r-classifier is used O(s) times, namely, the same number of times that Columnsort applies an r-sorter. A hardware implementation is proposed that runs in optimal O(s+log r) time and uses an O(r log r(s + log r)) work. The implementation shows that, when N = r log r, there is a classifier network solving the classification problem on N numbers in the same O(log r) time and using the same O(r log r) comparators as an r-classifier, thus saving a log r factor in the number of comparators over an (r log r)-classifier.
| Titolo: | Classifying matrices separating rows and columns | |
| Autore/i: | BERTOSSI, ALAN ALBERT; S. OLARIU; M. C. PINOTTI; S. Q. ZHENG | |
| Autore/i Unibo: | ||
| Anno: | 2004 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1109/TPDS.2004.16 | |
| Abstract: | The classification problem transforms a set of N numbers in such a way that none of the first N/2 numbers exceeds any of the last N/2 numbers. A comparator network that solves the classification problem on a set of r numbers is commonly called an r-classifier. This paper shows how the well-known Leighton’s Columnsort algorithm can be modified to solve the classification problem of N = rs numbers using an r-classifier instead of an r-sorting network. Overall, the r-classifier is used O(s) times, namely, the same number of times that Columnsort applies an r-sorter. A hardware implementation is proposed that runs in optimal O(s+log r) time and uses an O(r log r(s + log r)) work. The implementation shows that, when N = r log r, there is a classifier network solving the classification problem on N numbers in the same O(log r) time and using the same O(r log r) comparators as an r-classifier, thus saving a log r factor in the number of comparators over an (r log r)-classifier. | |
| Data prodotto definitivo in UGOV: | 2005-10-05 14:35:06 | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/853
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