A residual-based message passing algorithm for constraint satisfaction problems

Abstract

Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in tackling hard computational tasks in optimization, inference, and learning problems. In the context of constraint satisfaction problems (CSPs), when a control parameter (such as constraint density) is tuned, multiple threshold phenomena emerge, signaling fundamental structural transitions in their solution space. Finding solutions around these transition points is exceedingly challenging for algorithm design, where message passing algorithms suffer from a large message fluctuation far from convergence. Here we introduce a residual-based updating step into message passing algorithms, in which messages varying large between consecutive steps are given high priority in the updating process. For the specific example of model RB, a typical prototype of random CSPs with growing domains, we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost. Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.

arXiv comment11 pages, including 1 table and 10 figures

References in corpus (13)

• The Bethe lattice spin glass revisited
• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• Statistical physics of inference: Thresholds and algorithms
• Phase Transitions in the Coloring of Random Graphs
• The number of guards needed by a museum: A phase transition in vertex covering of random graphs
• Complex Systems: A Survey
• Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models
• Learning by message-passing in networks of discrete synapses
• Clusters of solutions and replica symmetry breaking in random k-satisfiability
• Mean-field message-passing equations in the Hopfield model and its generalizations
• Message passing for vertex covers
• The backtracking survey propagation algorithm for solving random K-SAT problems
• Consistency and Random Constraint Satisfaction Models