Optimal Compile-Time Multiprocessor Scheduling Based on the O–1 Linear Programming Algorithm with the Branch and Bound Technique

The problem of exploiting the effective utilization of a multiprocessor system essentially depends on optimal scheduling of parallel tasks onto the processors in the system. A recently proposed compile-time scheduling algorithm based on the 0–1 linear programming algorithm with the branch and bound technique, to produce optimal schedules, has the problems of communication link contention, nonoptimality, and modeling incompletely connected processor systems. In this paper, we present a modified version of this algorithm for producing contention-free optimal schedules for any arbitrary multiprocessor topology. To alleviate the impediments of large requirements of CPU time for the optimal scheduling algorithm, we have developed three new effective techniques, namely,processor isomorphism, look ahead pruning, andlower bound on the completion time of tasks. The performance of our algorithm is analyzed using DFT and LU decomposition methods as benchmarks.