Parallel sorting in two-dimensional VLSI models of computation

Abstract

The gradual refinement of a general approach to two-dimensional sorting, the shear-sort algorithm, to more sophisticated and specialized sorting algorithms on mesh-connected computers is described. The analysis of the shear-sort algorithm gives rise to a novel perspective of two-dimensional sorting, which seems to be a very powerful tool for developing efficient algorithms. The same methods can be extended for sorting in higher dimensions, for example, in the three-dimensional mesh. The concept of clean and dirty rows can be modified to clean and dirty planes (or hyperplanes for dimensions greater than three). Although only two schemes (purely recursive and iterative) are explicitly described, the reader may construct his own algorithm using similar technique and slight modifications. Designing an O(n) algorithm for sorting on a mesh becomes much simpler using the techniques developed.