A dominance relation enhanced branch-and-bound task allocation

We investigate the task allocation problem of allocating a parallel program on parallel processors with non-uniform communication latencies. A branch-and-bound algorithm with a dominance relation is proposed to obtain an optimal task assignment. The key observation on deriving the dominance relation is that tasks can be clustered according to communication weights. The dominance relation is effective to prune the search space when the task clustering boundary - a small cut - is met. The proposed algorithm is compared to the A*-algorithm for task allocation. Experiment shows that our proposed algorithm achieves a speed-up ranging from 1.02 to 1.68, depending on the degree of task clustering and parallelism. This shows the effectiveness of the proposed dominance relation.