Abstract: A framework for improving program performance by locality-enhancing transformations is presented. This framework is appropriate for modern high-performance machines that have a memory hierarchy. The invention orchestrates the flow of data through the memory hierarchy directly, and is thus able to overcome limitations of existing approaches. This new approach allows for efficient execution of imperfectly nested loop programs which are ubiquitous in numerical calculations and database operations, and it can be integrated into high-performance optimizing compilers.