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While many approaches have been proposed to analyze the problem of matrixmultiplication parallel computing, few of them address the problem onheterogeneous processor platforms. It still remains an open question onheterogeneous processor platforms to find the optimal schedule that balancesthe load within the heterogeneous processor set while minimizing the amount ofcommunication. A great many studies are based on rectangular partition, whereasthe optimality of rectangular partition as the basis has not been welljustified. In this paper, we propose a new method that schedules matrixmultiplication on heterogeneous processor platforms with the mixed co-designgoal of minimizing the total communication volume and the multiplicationcompletion time. We first present the schema of our layer based partition (LBP)method. Subsequently, we demonstrate that our approach guarantees minimalcommunication volume, which is smaller than what rectangular partition canreach. We further analyze the problem of minimizing the task completion time,with network topologies taken into account. We solve this problem in bothsingle-neighbor network case and multi-neighbor network case. Insingle-neighbor network cases, we propose an equality based method to solveLBP, and simulation shows that the total communication volume is reduced by 75%from the lower bound of rectangular partition. In multi-neighbor network cases,we formulate LBP as a Mixed Integer Programming problem, and reduce the totalcommunication volume by 81% through simulation. To summarize, this is apromising perspective of tackling matrix multiplication problems onheterogeneous processor platforms.

Layer Based Partition for Matrix Multiplication on Heterogeneous Processor Platforms