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(N⁴)-time algorithm for determining the dynamic controllability of arbitrary STNUs, where N is the number of time points. Morris suggested that additional O(N⁴)-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(N²) space and O(N⁴) time. The O(N⁴)-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(N³) per iteration. Furthermore, the most costly computations - O(N³) per iteration - are done while waiting for the next execution event to occur, whereas the time-critical computations require only O(N²) per iteration.