Optimization of a Class of Multi-Dimensional Integrals on Parallel Machines

Multi-dimensional summations involving products of arrays arise in certain kinds of computational physics calculations that model electronic structure. Besides the issue of optimal distribution of the arrays among the processors, there is also scope for reordering of the operations using algebraic properties (commutativity, associativity, distributive law) to significantly reduce the number of operations executed. A framework for optimization of computational cost and communication cost has been developed, that can be used to synthesize efficient code.