A Multistage Linear Array Assignment Problem

Implementation of certain algorithms on parallel computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomiailybounded algorithms are developed for the case of two-stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NPcomplete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented for a variety of test problems. Empirical results also, demonstrato that one of the heuristic procedures is especially effective in practice. < (* ) 'This research was supported in part by the National Aeronautics and Space Administration under NASA Contract Nos. NAS1-18107 and NAS1-18605 and by the Air Force Office of Scientific Research under Contract No. AFOSR 88-0117 while the first author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665.