Directional Consistency for Continuous Numerical Constraints

TL;DR

This paper analyzes a novel algorithm for continuous constraints that avoids decomposition, demonstrating its efficiency and relation to directional bounds consistency, supported by theoretical analysis and experimental validation.

Contribution

It shows that the new algorithm enforces a form of directional bounds consistency on continuous constraints, providing both theoretical insights and empirical performance comparisons.

Findings

The algorithm is more efficient than traditional decomposition methods.

It enforces a form of directional bounds consistency.

Experimental results validate theoretical advantages.

Abstract

Bounds consistency is usually enforced on continuous constraints by first decomposing them into binary and ternary primitives. This decomposition has long been shown to drastically slow down the computation of solutions. To tackle this, Benhamou et al. have introduced an algorithm that avoids formally decomposing constraints. Its better efficiency compared to the former method has already been experimentally demonstrated. It is shown here that their 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 algorithm is analyzed in this framework, and compared with algorithms that enforce bounds consistency. These theoretical results are eventually contrasted with new experimental results on standard benchmarks from the interval constraint community.