Speeding Up the RUL¯ Dynamic-Controllability-Checking Algorithm for Simple Temporal Networks with Uncertainty

A Simple Temporal Network with Uncertainty (STNU) in- cludes real-valued variables, called time-points; binary differ- ence constraints on those time-points; and contingent links that represent actions with uncertain durations. STNUs have been used for robot control, web-service composition, and business processes. The most important property of an STNU is called dynamic controllability (DC); and algorithms for checking this property are called DC-checking algorithms. The DC- checking algorithm for STNUs with the best worst-case time- complexity is the RUL− algorithm due to Cairo, Hunsberger and Rizzi. Its complexity is O(mn + k2n + kn log n), where n is the number of time-points, m is the number of constraints, and k is the number of contingent links. It is expected that this worst-case complexity cannot be improved upon. However, this paper provides a new algorithm, called RUL2021, that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation.