Converting Simple Temporal Networks with Uncertainty into Minimal Equivalent Dispatchable Form

Abstract

A Simple Temporal Network with Uncertainty (STNU) is a structure for representing and reasoning about time constraints on actions that may have uncertain durations. An STNU is dynamically controllable (DC) if there exists a dynamic strategy for executing the network that guarantees that all of its constraints will be satisfied no matter how the uncertain durations turn out---within their specified bounds. However, such strategies typically require exponential space. Therefore, converting a DC STNU into a so-called dispatchable form for practical applications is essential. The relevant portions of a real-time execution strategy for a dispatchable STNU can be incrementally constructed during execution, requiring only O(n²) space, while also providing maximum flexibility and minimal computation during the execution of the network. Although existing algorithms can generate equivalent-dispatchable STNUs, they do not guarantee a minimal number of edges in the STNU graph. Since the number of edges directly impacts the computations during execution, this paper presents a novel algorithm for converting any dispatchable STNU into an equivalent dispatchable network having a minimal number of edges. The complexity of the algorithm is O(k n³), where k is the number of actions with uncertain durations, and n is the number of timepoints in the network. The paper also provides an empirical evaluation of the reduction of edges obtained by the impact of the new algorithm.