Algorithms for Mesh Connected Computers

Abstract

This chapter presents algorithms for solving a number of problems on mesh connected computers. The problems that were selected fall into the categories of basic communication operations, image processing, and scientific applications. The algorithms in this section will be for the plain mesh connected computer. A plain mesh connected computer operates in an SIMD mode. The PEs use uniform addressing in accessing their memories (all PEs access the same local memory location at any given time), and communication is weak and uniform (each PE can send a message to only one neighbor at a time, and all PEs communicate in the same direction). The PEs can be selectively disabled by using mask registers. The top and bottom rows and the leftmost and rightmost columns are connected, so that the interconnections logically form a torus. It should be noted, however, that a machine that does not have these “wraparound” connections can simulate a machine that does have them with only a constant factor increase in time. In particular, consider a P ^1/2 × P ^1/2 mesh connected computer without wraparound connections, where P ^½ is an even integer. Let the function f(i) be defined such that f(i) = 2i, if 0 ≤ i < P ^½/2, and f(i) = 2P ^½ − 2i − 1, if P ^½ ≤ i < P ^½. Each processor (i, j) of a P ^½ × P ^½ mesh with wraparounds is mapped to processor [f(i), f(j)] of a P ^½ × P ^½ mesh without wraparounds.