Classifying Matrices Separating Rows and Columns

• Authors: A. A. Bertossi;S. Olariu;M. C. Pinotti;Si-Qing Zheng
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 2004

The classification problem transforms a set of N numbers in such a way that none of the first \frac{N}{2} numbers exceeds any of the last \frac{N}{2} numbers. A comparator network that solves the classification problem on a set of r numbers is commonly called an r{\hbox{-}}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{\hbox{-}}{\rm{classifier}} instead of an r{\hbox{-}}{\rm{sorting}} network. Overall, the r{\hbox{-}}{\rm{classifier}} is used O(s) times, namely, the same number of times that Columnsort applies an r{\hbox{-}}{\rm{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{\hbox{-}}{\rm{classifier}}, thus saving a \log r factor in the number of comparators over an (r\log r){\hbox{-}}{\rm{classifier}}.