A Faster Execution Algorithm for Dynamically Controllable STNUs

A Simple Temporal Network with Uncertainty (STNU) is a data structure for representing and reasoning about temporal constraints where the durations of certain temporal intervals-the contingent links-are only discovered during execution. The most important property of anSTNU is whether it is dynamically controllable (DC)-that is, whether there exists a strategy for executing time-points that will guarantee that all constraints will be satisfied no matter how the durations of the contingent links turn out. The fastest DC-checking algorithm reported so far is the O(N
⁴
)-time algorithm due to Morris (2006). Huns Berger (2010) presented an O(N
⁴
)-time execution algorithm for dynamically controllable STNUs, the fastest reported so far. This paper improves upon that algorithm, presenting an O(N
³
)-time execution algorithm for DC STNUs. The increase in speed is due to more efficient management of the so-called ``wait'' constraints, which must be removed from the network whenever the corresponding contingent link completes.