Controlled propagation in continuous numerical constraint networks

Local consistency is usually enforced on continuous constraints by decomposing them beforehand into so-called primitive constraints. It has long been observed that such a decomposition drastically slows down the computation of solutions. Five years ago, Benhamou et al. introduced an algorithm that avoids formally decomposing constraints, and whose efficiency is often on a par with state-of-the-art methods. It is shown here that this algorithm implements a strategy to enforce on a continuous constraint a consistency akin to directional bounds consistency as introduced by Dechter and Pearl for discrete problems. The actual impact of decomposition is also thoroughly analyzed by means of new experimental results.