Efficient processing of simple temporal networks with uncertainty: algorithms for dynamic controllability verification

Temporal formalisms are essential for reasoning about actions that are carried out over time. The exact durations of such actions are generally hard to predict. In temporal planning, the resulting uncertainty is often worked around by only considering upper bounds on durations, with the assumption that when an action happens to be executed more quickly, the plan will still succeed. However, this assumption is often false: if we finish cooking too early, the dinner will be cold before everyone is ready to eat. Using simple temporal networks with uncertainty (STNU) , a planner can correctly take both lower and upper duration bounds into account. It must then verify that the plans it generates are executable regardless of the actual outcomes of the uncertain durations. This is captured by the property of dynamic controllability (DC), which should be verified incrementally during plan generation. Recently a new incremental algorithm for verifying dynamic controllability was proposed: EfficientIDC, which can verify if an STNU that is DC remains DC after the addition or tightening of a constraint (corresponding to a new action being added to a plan). The algorithm was shown to have a worst case complexity of O(n^4) for each addition or tightening. This can be amortized over the construction of a whole STNU for an amortized complexity in O(n^3) . In this paper we improve the EfficientIDC algorithm in a way that prevents it from having to reprocess nodes. This improvement leads to a lower worst case complexity in O(n^3) .