Fast solution of NP-hard coloring problems on large random graphs

Andrea Bedini (1) , Jesper Jacobsen (2)

1 INFN - Istituto Nazionale di Fisica Nucleare, Sezione di Milano
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

Combining tree decomposition and transfer matrix techniques provides a highly efficient and very general algorithm for computing exact partition functions of statistical models defined on large graphs. We illustrate this by considering the hard problem of computing the exact number of vertex colorings for randomly generated planar graphs with up to N = 100 vertices.

Mots clés: computational complexity; transfer matrix; tree decomposition; chromatic polynomial

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]; Combinatoire [math.CO]; Complexité [cs.CC]

Andrea Bedini, Jesper Jacobsen. Fast solution of NP-hard coloring problems on large random graphs. 2010. ⟨hal-00466411v1⟩