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ABSTRACT
<p><b>Abstract</b>—The classification problem transforms a set of <tmath>N</tmath> numbers in such a way that none of the first <tmath>\frac{N}{2}</tmath> numbers exceeds any of the last <tmath>\frac{N}{2}</tmath> numbers. A comparator network that solves the classification problem on a set of <tmath>r</tmath> numbers is commonly called an <tmath>r{\hbox{-}}classifier</tmath>. This paper shows how the well-known Leighton's Columnsort algorithm can be modified to solve the classification problem of <tmath>N=rs</tmath> numbers, with <tmath>1 \le s \le r</tmath>, using an <tmath>r{\hbox{-}}{\rm{classifier}}</tmath> instead of an <tmath>r{\hbox{-}}{\rm{sorting}}</tmath> network. Overall, the <tmath>r{\hbox{-}}{\rm{classifier}}</tmath> is used <tmath>O(s)</tmath> times, namely, the same number of times that Columnsort applies an <tmath>r{\hbox{-}}{\rm{sorter}}</tmath>. A hardware implementation is proposed that runs in optimal <tmath>O(s + \log r)</tmath> time and uses an <tmath>O(r\log r(s + \log r))</tmath> work. The implementation shows that, when <tmath>N= r\log r</tmath>, there is a classifier network solving the classification problem on <tmath>N</tmath> numbers in the same <tmath>O(\log r)</tmath> time and using the same <tmath>O(r\log r)</tmath> comparators as an <tmath>r{\hbox{-}}{\rm{classifier}}</tmath>, thus saving a <tmath>\log r</tmath> factor in the number of comparators over an <tmath>(r\log r){\hbox{-}}{\rm{classifier}}</tmath>.</p>
INDEX TERMS
Comparator network, classifier, classification problem, hardware algorithm.
CITATION

A. A. Bertossi, M. C. Pinotti, S. Olariu and S. Zheng, "Classifying Matrices Separating Rows and Columns," in IEEE Transactions on Parallel & Distributed Systems, vol. 15, no. , pp. 654-665, 2004.
doi:10.1109/TPDS.2004.16
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