Reducing Inter Iteration Dependency Delays in Multiprocessor Systems for Large Graphs

Applications such as image processing, fluid mechanics, and weather forecasting require high computer performance. Researchers and designers in those areas are looking for solutions to multi-dimensional problems through the use of parallel computers and/or specialized hardware. It is known that in highly parallel computers communication is often the limiting execution speed bottleneck. While the problem of calculating and minimizing communication costs due to loop data dependencies has been widely studied, such research has involved changing the way iterations are partitioned, not modifying the graph or loop data dependencies themselves. This paper uses algorithms that minimize loop data communication for multi-dimensional graphs by modifying the structure of the input graph and changing the distribution of the loop dependencies using multi-dimensional retiming. These algorithms are extended to large graphs and compared for effectiveness. Results are shown which illustrate the efficiency of the algorithms as well as the savings achieved for large graphs.