Comparison of Static and Runtime Resource Allocation Strategies for Matrix Multiplication

The tremendous increase in the size and heterogeneity of supercomputers makes it very difficult to predict the performance of a scheduling algorithm. In this context, relying on purely static scheduling and resource allocation strategies, that make scheduling and allocation decisions based on the dependency graph and the platform description, is expected to lead to large and unpredictable make spans whenever the behavior of the platform does not match the predictions. For this reason, the common practice in most runtime libraries is to rely on purely dynamic scheduling strategies, that make short-sighted scheduling decisions at runtime based on the estimations of the duration of the different tasks on the different available resources and on the state of the machine. In this paper, we consider the special case of Matrix Multiplication, for which a number of static allocation algorithms to minimize the amount of communications have been proposed. Through a set of extensive simulations, we analyse the behaviour of static, dynamic, and hybrid strategies, and we assess the possible benefits of introducing more static knowledge and allocation decisions in runtime libraries.