Incremental Dynamic Controllability in Cubic Worst-Case Time

Abstract

It is generally hard to predict the exact duration of an action. Uncertainty in durations is often modeled in temporal planning by the use of upper bounds on durations, with the assumption that if 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. Simple Temporal Problems with Uncertainty (STPUs) allow us to model such situations. An STPU-based planner must verify that the plans it generates are executable, captured by the property of dynamic controllability. The Efficient IDC (EIDC) algorithm can do this incrementally during planning, with an amortized complexity per step of O(n3) but a worst-case complexity per step of O(n4). In this paper we show that the worst-case run-time of EIDC does occur, leading to repeated reprocessing of nodes in the STPU while verifying the dynamic controllability property. We present a new version of the algorithm, EIDC2, which through optimal ordering of nodes avoids the need for reprocessing. This gives EIDC2 a strictly lower worst-case run-time, making it the fastest known algorithm for incrementally verifying dynamic controllability of STPUs.