Parallel domain decomposition and load balancing using space-filling curves

Partitioning techniques based on space filling curves have received much recent attention due to their low running time and good load balance characteristics. The basic idea underlying these methods is to order the multidimensional data according to a space filling curve and partition the resulting one dimensional order. However, space filling curves are defined for points that lie on a uniform grid of a particular resolution. It is typically assumed that the coordinates of the points are representable using a fixed number of bits, and the run times of the algorithms depend upon the number of bits used. We present a simple and efficient technique for ordering arbitrary and dynamic multidimensional data using space filling curves and its application to parallel domain decomposition and load balancing. Our technique is based on a comparison routine that determines the relative position of two points in the order induced by a space filling curve. The comparison routine could then be used in conjunction with any parallel sorting algorithm to effect parallel domain decomposition.