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Classifying matrices separating rows and columns

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4 Author(s)
Bertossi, A.A. ; Dept. of Comput. Sci., Bologna Univ., Italy ; Olariu, S. ; Pinotti, M.C. ; Si-Qing Zheng

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. We show how the well-known Leighton's Columnsort algorithm can be modified to solve the classification problem of N=rs numbers, with 1 ≤ s ≤ 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+logr) time and uses an O(rlogr(s + logr)) work. The implementation shows that, when N= rlogr, there is a classifier network solving the classification problem on N numbers in the same O(logr) time and using the same O(rlogr) comparators as an r-classifier, thus saying a logr factor in the number of comparators over an (rlogr)-classifier.

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:15 ,  Issue: 7 )