On the complexity of task allocation

A detailed study is presented on the combinatorial optimization problem of allocating parallel tasks to a parallel computer. Depending on two application/machine-specific parameters, both a sequential and a parallel optimal allocation phase are shown to exist. A sudden “phase” transition is observed if one of these parameters is varied. Simulated annealing is used to find the optimal allocations, which is justified by the self-similar structure of the task allocation energy landscape. It is shown that the difficulty of finding optimal allocations behaves anomalously near the transition, analogous to critical slowing down of simulated equilibration at second-order phase transitions. © 1997 John Wiley & Sons, Inc.