A Fast Incremental Algorithm for Managing the Execution of Dynamically Controllable Temporal Networks

A Simple Temporal Network with Uncertainty (STNU) is a network of time points and temporal constraints in which the durations of certain temporal intervals - the contingent links-are bounded, but not controllable. An STNU is dynamically controllable if there is a real-time strategy for executing its non-contingent time points that guarantees the consistency of the network no matter how the durations of the contingent links turn out. Morris presented an O(N
⁴
)-time algorithm for determining the dynamic controllability of arbitrary STNUs, where N is the number of time points. Morris suggested that additional O(N
⁴
)-time computation might be needed to prepare a dynamically controllable network for execution, with all computations done in advance of execution. Instead, this paper shows that an STNU that has passed Morris' algorithm is already prepared for execution. The paper presents an incremental, real-time execution algorithm that is guaranteed to successfully execute the time points in a dynamically controllable STNU using O(N
²
) space and O(N
⁴
) time. The O(N
⁴
)-time computations are not done in advance of execution, but instead are spread out over the entire time that time points in the network are being executed: N iterations of O(N
³
) per iteration. Furthermore, the most costly computations - O(N
³
) per iteration - are done while waiting for the next execution event to occur, whereas the time-critical computations require only O(N
²
) per iteration.