Loop storage optimization for dataflow machines

Abstract

In scientific computation, loops are frequently used to compute large quantities of data organized in arrays. On a dataflow machine, the main challenge is how to maximally exploit fine-grain parallelism to speed up loop execution while not incurring excessive storage space overhead than what is necessary.

The main contributions of this paper include:

• The minimum storage requirement to support the maximum computation rate is analyzed and a storage minimization scheme called limited balancing is introduced. The basic intuition is that, since maximum computation rate is dominated by critical cycles in the loop, we should not allocate extra storage beyond a certain limit bounded by the ratios of the critical cycles. In other words, all cycles should be balanced to have the same balancing ratio.

• The limited balancing problem is formulated as a integer linear programming problem. An efficient solution of the problem is presented. It reduces the problem to a network flow problem called “minimum circulation flow” problem. Therefore, a polynomial time algorithm is established for the solution of the linear relaxation of the limited balancing problem.

Our formal framework is developed under a FIFO dataflow model where each are in the dataflow graph is a FIFO queue of certain size. we establish the maximum computation rate of a loop under earliest firing schedule, and show that the maximum computation rate is dominated by the critical cycles of the dataflow graph. We discuss how our results may be applied to both the static dataflow model and the dynamic dataflow model.