Metrics and models for reordering transformations

Irregular applications frequently exhibit poor performance on contemporary computer architectures, in large part because of their inefficient use of the memory hierarchy. Run-time data, and iteration-reordering transformations have been shown to improve the locality and therefore the performance of irregular benchmarks. This paper describes models for determining which combination of run-time data- and iteration-reordering heuristics will result in the best performance for a given dataset. We propose that the data- and iteration-reordering transformations be viewed as approximating minimal linear arrangements on two separate hypergraphs: a spatial locality hypergraph and a temporal locality hypergraph. Our results measure the efficacy of locality metrics based on these hypergraphs in guiding the selection of data-and iteration-reordering heuristics. We also introduce new iteration- and data-reordering heuristics based on the hypergraph models that result in better performance than do previous heuristics.