Classical Dynamic Controllability Revisited - A Tighter Bound on the Classical Algorithm

Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are uncontrollable and determined by nature, as is often the case for actions in planning. It is essential to verify that such networks are dynamically controllable (DC) -- executable regardless of the outcomes of uncontrollable durations -- and to convert them to an executable form. In this paper we use insights from incremental DC verification algorithms to re-analyze the original DC verification algorithm. We show that this algorithm, first thought to be pseudo-polynomial and subsumed by an $O(n^5)$ algorithm and later an $O(n^4)$ algorithm, is in fact $O(n^4)$ given a small modification. This makes the algorithm attractive once again, given its basis in a less complex and more intuitive theory. It is also the only algorithm with a direct correctness proof. Finally, we discuss a change reducing the amount of work performed by the algorithm.