| Abstract: | In irregular scientific computational problems one is periodically forced to choosea delay point where some overhead cost is suffered to ensure correctness, or to improve subsequent performance. Examples of delay points are problem remappings, and global synchronizations. One sometimes has considerable latitude in choosing the placement and frequency of delay points; we consider the problem of scheduling delay points so as to minimize the overal execution time. We illustrate the problem with two examples, a regridding method which changes the problem discretization during the course of the computation, and a method for solving sparse triangular systems of linear equations. We show that one can optimally choose delay points in polynomial time using dynamic programming. However, the cost models underlying this approach are often unknown. We consequently examine a scheduling heuristic based on maximizing performance locally, and empirically show it to be nearly optimal on both problems. We explain this phenomenon analytically by identifying underlying assumptions which imply that overall performance is maximized asymptotically if local performance is maximized.This research was supported in part by the National Aeronautics and Space Administration under NASA contract NAS1-18107 while the author consulted at ICASE, Mail Stop 132C, NASA Langley Research Center, Hampton, Virginia 23665.Supported in part by NASA contract NAS1-18107, the Office of Naval Research under Contract No. N00014-86-K-0654, and NSF Grant DCR 8106181. |
