Efficient Message Passing and Propagation of Simple Temporal Constraints: Results on Semi-Structured Networks

Abstract

The familiar 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., 4STP). However, none of these existing methods exploit effectively the treedecomposition 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 a set of continuous domains. We first 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 4STP and SR-PC. Empirical results validate the efficiency of Prop-STP, demonstrating performance comparable to 4STP, in cases where the constraint network is known to have small tree-width, such as those that arise in Hierarchical Task Network planning problems.