Invariant Polydiagonal Subspaces of Matrices and Constraint Programming

TL;DR

This paper characterizes invariant polydiagonal subspaces of matrices using coloring vectors, formulates a constraint satisfaction problem, and demonstrates that solving it with modern solvers outperforms previous algorithms, with applications in graph theory and dynamical systems.

Contribution

It introduces a new formulation of invariant polydiagonal subspaces as a constraint satisfaction problem using coloring vectors, enabling more efficient solutions.

Findings

Constraint satisfaction formulation outperforms existing algorithms

Coloring vectors provide an easy way to describe invariant subspaces

Applications in graph theory and dynamical systems

Abstract

In a polydiagonal subspace of the Euclidean space, certain components of the vectors are equal (synchrony) or opposite (anti-synchrony). Polydiagonal subspaces invariant under a matrix have many applications in graph theory and dynamical systems, especially coupled cell networks. We describe invariant polydiagonal subspaces in terms of coloring vectors. This approach gives an easy formulation of a constraint satisfaction problem for finding invariant polydiagonal subspaces. Solving the resulting problem with existing state-of-the-art constraint solvers greatly outperforms the currently known algorithms.