Computational Aspects of Reordering Plans

This article studies the problem of modifying the action ordering of a plan in order to optimise the plan according to various criteria. One of these criteria is to make a plan less constrained and the other is to minimize its parallel execution time. Three candidate de nitions are proposed for the rst of these criteria, constituting a sequence of increasing optimality guarantees. Two of these are based on deordering plans, which means that ordering relations may only be removed, not added, while the third one uses reordering, where arbitrary modi cations to the ordering are allowed. It is shown that only the weakest one of the three criteria is tractable to achieve, the other two being NP-hard and even di cult to approximate. Similarly, optimising the parallel execution time of a plan is studied both for deordering and reordering of plans. In the general case, both of these computations are NP-hard. However, it is shown that optimal deorderings can be computed in polynomial time for a class of planning languages based on the notions of producers, consumers and threats, which includes most of the commonly used planning languages. Computing optimal reorderings can potentially lead to even faster parallel executions, but this problem remains NP-hard and di cult to approximate even under quite severe restrictions.