English

Solving Constraint Satisfaction Problems through Belief Propagation-guided decimation

Artificial Intelligence 2019-06-05 v3 Disordered Systems and Neural Networks Statistical Mechanics Computational Complexity

Abstract

Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is run after each step. Its outcome provides an heuristic to make choices at next step. This approach has been referred to as `decimation,' with reference to analogous procedures in statistical physics. The behavior of decimation procedures is poorly understood. Here we consider a simple randomized decimation algorithm based on belief propagation (BP), and analyze its behavior on random k-satisfiability formulae. In particular, we propose a tree model for its analysis and we conjecture that it provides asymptotically exact predictions in the limit of large instances. This conjecture is confirmed by numerical simulations.

Keywords

Cite

@article{arxiv.0709.1667,
  title  = {Solving Constraint Satisfaction Problems through Belief Propagation-guided decimation},
  author = {Andrea Montanari and Federico Ricci-Tersenghi and Guilhem Semerjian},
  journal= {arXiv preprint arXiv:0709.1667},
  year   = {2019}
}

Comments

10 pages, 4 figures. A longer version can be found as arXiv:0904.3395 [cond-mat.dis-nn]

R2 v1 2026-06-21T09:16:21.947Z