New Techniques for Checking Dynamic Controllability of Simple Temporal Networks with Uncertainty

Abstract

A Simple Temporal Network with Uncertainty (STNU) is a structure for representing time-points, temporal constraints, and temporal intervals with uncertain—but bounded—durations. The most important property of an STNU is whether it is dynamically controllable (DC)—that is, whether there exists a strategy for executing its time-points such that all constraints will necessarily be satisfied no matter how the uncertain durations turn out. Algorithms for checking from scratch whether STNUs are dynamically controllable are called (full) DC-checking algorithms. Algorithms for checking whether the insertion of one new constraint into an STNU preserves its dynamic controllability are called incremental DC-checking algorithms. This paper introduces novel techniques for speeding up both full and incremental DC checking. The first technique, called rotating Dijkstra, enables constraints generated by propagation to be immediately incorporated into the network. The second uses novel heuristics that exploit the nesting structure of certain paths in STNU graphs to determine good orders in which to propagate constraints. The third technique, which only applies to incremental DC checking, maintains information acquired from previous invocations to reduce redundant computation. The most important contribution of the paper is the incremental algorithm, called Inky, that results from using these techniques. Like its fastest known competitors, Inky is a cubic-time algorithm. However, a comparative empirical evaluation of the top incremental algorithms, all of which have only very recently appeared in the literature, must be left to future work.