Efficient Variable Elimination for Semi-Structured Simple Temporal Networks with Continuous Domains

Abstract

The Simple Temporal Network (STN) is a widely used framework for reasoning about quantitative temporal constraints over variables with continuous or discrete domains. The inference tasks of determining consistency and deriving the minimal network are traditionally achieved by graph algorithms (e.g. Floyd-Warshall, Johnson) or by iteration of narrowing operators (e.g. ΔSTP). None of these methods exploits effectively the tree-decomposition structure of the constraint graph of an STN. Methods based on variable elimination (e.g. adaptive consistency) can exploit this structure, but have not been applied to STNs as far as they could, in part because it is unclear how to efficiently pass the ‘messages’ over continuous domains. We show that for an STN, these messages can be represented compactly as sub-STNs. We then present an efficient message-passing scheme for computing the minimal constraints of an STN. Analysis of this algorithm, Prop-STP, brings formal explanation of the performance of the existing STN solvers ΔSTP and SR-PC. Empirical results validate the efficiency of Prop-STP, demonstrating performance comparable to ΔSTP, in cases where the constraint graph is known to have small tree width, such as those that arise during Hierarchical Task Network planning.