Overview and extensions of a system for routing directed graphs on SIMD architectures

A method is given for parallelizing the problems of directed graphs on a single-instruction multiple-data (SIMD) machine model that uses only nearest-neighbor connections for communication and has no facility for local indirect addressing. Each vertex of the graph is assigned to a processor in the machine. Rules for labeling are introduced that support the use of a simple algorithm for movement of data along the edges of the graph. Additional algorithms are defined for addition and deletion of edges. Modifying or adding a new edge takes the same time as parallel traversal. This combination of architecture and algorithm defines a system that is relatively simple to build and can do fast graph processing. All edges can be traversed in parallel in time O( T), where T is empirically proportional to the average path length in the embedding times the average degree of the graph. An extension to the above method is presented which allows for enhanced performance by allowing some broadcasting capabilities