Lower bounding techniques for the multiprocessor scheduling problem with communication delay

This paper proposes two techniques for obtaining a sharp lower bound for the multiprocessor scheduling problem (MSP) with nonnegligible communication delay. In the proposed techniques, we apply the notion of inevitable communication delay to obtain a nontrivial lower bound on the scheduling length. The effectiveness of the derived bound is evaluated by conducting experiments on several randomly generated instances. By the results of the experiments, it is shown that the proposed techniques generate a very sharp lower bound that is at least 97.5% of an upper bound, when the number of processors is not very small (e.g., at least 10) and the maximum communication cost is not very large (e.g., less than or equal to the minimum execution cost).