Lower and upper bounds on time for multiprocessor optimal schedules

K. Kumar Jain, V. Rajaraman
1994 IEEE Transactions on Parallel and Distributed Systems  
The lower and upper bounds on the minimum time needed to process a given directed acyclic task graph for a given number of processors are derived. It is proved that the proposed lower bound on time is not only sharper than the previously known values but also easier to calculate. The upper bound on time, which is useful in determining the worst case behavior of a given task graph, is presented for the first time. The lower and upper bounds on the minimum number of processors required to process
more » ... required to process a given task graph in the minimum possible time are also derived. It is seen with a number of randomly generated dense task graphs that the lower and upper bounds we derive are equal, thus giving the optimal time for scheduling directed acyclic task graphs on a given set of processors. Zndex Terms-Bounds on number of processors, bounds on time, multiprocessing, optimal scheduling, parallel processing, performance evaluation, scheduling directed acyclic task graphs
doi:10.1109/71.298216 fatcat:3gaqt7w6yfapnkkejhmjmqeygm