Time- and VLSI-optimal sorting on enhanced meshes

Abstract

Sorting is a fundamental problem with applications in all areas of computer science and engineering. In this work, we address the problem of sorting on mesh connected computers enhanced by endowing each row and each column with its own dedicated high-speed bus. This architecture, commonly referred to as a mesh with multiple broadcasting, is commercially available and has been adopted by the DAP family of multiprocessors. Somewhat surprisingly, the problem of sorting m, (m/spl les/n), elements on a mesh with multiple broadcasting of size /spl radic/n/spl times//spl radic/n has been studied, thus far, only in the sparse case, where m/spl isin//spl Theta/(/spl radic/n) and in the dense case, where m/spl isin//spl Theta/O(/spl radic/n). Yet, many applications require using an existing platform of size /spl radic/n/spl times//spl radic/n for sorting m elements, with /spl radic/n<m/spl les/n. Our main contribution is to present the first known adaptive time- and VLSI-optimal sorting algorithm for meshes with multiple broadcasting. Specifically we show that, for every choice of a constant 0</spl epsiv//spl les/ 1/2 , it is possible to sort m elements, n/sup 1/2 +/spl epsiv///spl les/m/spl les/n, stored in the leftmost [m//spl radic/n] columns of a mesh with multiple broadcasting of size /spl radic/n/spl times//spl radic/n in /spl Theta/(m//spl radic/n) time.