A practical processor self-scheduling scheme, trapezoid self-scheduling, is proposed for arbitrary parallel nested loops in shared-memory multiprocessors. Generally, loops are the richest source of parallelism in parallel programs. To dynamically allocate loop iterations to processors, one may achieve load balancing among processors at the expense of run-time scheduling overhead. By linearly decreasing the chunk size at run time, the best tradeoff between the scheduling overhead and balanced workload can be obtained in the proposed trapezoid self-scheduling approach. Due to its simplicity and flexibility, this approach can be efficiently implemented in any parallel compiler. The small and predictable number of chores also allow efficient management of memory in a static fashion. The experiments conducted in a 96-node Butterfly GP-1000 clearly show the advantage of the trapezoid self-scheduling over other well-known self-scheduling approaches.>

Data dependence uniformization, a method for overcoming the difficulties in parallelizing a doubly nested loop with irregular dependence constraints is proposed. This approach is based on the concept of vector decomposition. A simple set of basic dependences is developed from which all dependence constraints can be composed. The set of basic dependences is added to every iteration to replace all original dependences so that the dependence constraints become uniform. An efficient synchronization method is presented to obey the uniform dependence constraints in every iteration.>