Recent algorithmic advances in simple temporal networks with uncertainty: From faster controllability checking to faster execution

Abstract

This paper advances the state of the art in the dynamic controllability (DC) and dispatchability of Simple Temporal Networks with Uncertainty (STNUs) through four key contributions.

First, findSRNC is an algorithm that identifies semi-reducible negative cycles in non-dynamically controllable STNUs. Running in $O(mn+k^{2}n+kn\log n)$ time (matching the fastest DC-checking algorithms), it handles repeated edges and uses polynomial space, even when cycles might contain exponentially many edges.

Second, minDisp${}_{\mathrm{ESTNU}}^{+}$ is an algorithm that improves dispatchability computation for STNUs from $O\left(k{n}^3\right)$ to $O(n^3+k^{2}n\log n)$ time. It outputs dispatchable Extended STNUs (ESTNUs) having minimal numbers of edges, which is crucial for subsequent real-time execution.

Third, the Canonical Form of Nested Diamond Structures in Dispatchable ESTNUs is a rigorous theory that facilitates correctness proofs for dispatchability algorithms. It also helped reveal and correct a flaw in a previously published algorithm.

Fourth, our empirical evaluation using improved open-source implementations demonstrates the practical effectiveness of our algorithms.

These contributions address fundamental computational bottlenecks in temporal planning systems, enabling more efficient reasoning about uncertain timing constraints while providing real-time guarantees required for robotics, scheduling, and automated planning applications.