The parallel assignment problem redefined

The parallel assignment problem is slightly redefined using a subtler cost function that tends to reduce the number of extra assignments required. It is shown that the new problem, like the classical, is NP-hard. The new problem is then solved for the restricted case of assignment from invertible functions of single variables. For this restricted case and optimum solution can be found in linear time for both the classical problem and the new problem. However, the number of extra assignments required for the classical problem is equal to the number of cycles in the dependency graph, while in the new problem it is equal to the number of isolated cycles in the dependency graph which may be less