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, with 1 \le s \le r, 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 þ 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

Classifying matrices separating rows and columns

PINOTTI, Maria Cristina;
2004

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, with 1 \le s \le r, 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 þ 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
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/120739
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