Memory optimization for parallel functional programs

Parallel functional languages use single valued variables to avoid semantically irrelevant data dependence constraints. Programs containing iterations that redefine variables in a procedural language have the corresponding variables declared with additional dimensions in a single assignment language. This extra temporal dimension, unless optimized, requires an exorbitant amount of memory and in parallel programs imposes a large delay between the data producer and consumers. For certain loop arrangements, a window containing a few elements of the dimension can be created. Usually, there are many ways for defining a loop arrangement in an implementation of a functional program and a trade-off between the memory saving and the needed level of parallelism has to be taken into account when selecting the implementation. In this paper we prove that the problem of determining the best loop arrangement by partitioning the dependence graph is NP-hard. In addition, we describe a heuristic for solving this problem. Finally, we present examples of parallel functional programs in which the memory optimization results in reducing the local and shared memory requirements and communication delays.