The GDE Method

Abstract

We present in this chapter the generalized dimension exchange (GDE) method for load balancing in multiprocessors. In hypercube-structured multiprocessors, the dimension exchange method works in the way that each processor compares its workload with those of its nearest neighbors one after another. At each of these comparisons, the processor would try to equalize its workload with its neighbor’s. To do this systematically, all the processors could follow the order as implied by the dimension indices of the hypercube: equalizing workload with the neighbor along dimension 1, and then along dimension 2, and so on. In arbitrary-structure systems, the dimension can be defined by edge-coloring techniques. With edge-coloring [65], the edges of a given system graph are colored with some minimum number of colors such that no two adjoining edges are of the same color. A “dimension” is then defined to be the collection of all edges of the same color. During each iteration sweep, all colors/dimensions are considered in turn. Since no two adjoining edges have the same color, each node needs to deal with at most one neighbor at each iteration step (each step corresponds to one color; a sweep corresponds to going through all the colors once).