Reduction of constraint systems

TL;DR

This paper presents a graph-based method for decomposing large algebraic constraint systems into smaller, manageable subsystems, improving efficiency and aiding debugging in geometric modeling.

Contribution

It introduces a polynomial-time decomposition technique for constraint systems using bipartite graphs, enabling better analysis and resolution of complex geometric constraints.

Findings

Decomposition speeds up solving reducible systems.

Graph-based approach identifies well, over-, and underconstrained subsystems.

Method facilitates debugging of constraint systems.

Abstract

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into well constrained, over-, and underconstrained subsystems. This paper also gives an efficient method to decompose well constrained systems into irreducible ones. These decompositions greatly speed up the resolution in case of reducible systems. They also allow debugging systems of constraints.