On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms

TL;DR

This paper develops a cavity method for analyzing belief propagation guided decimation algorithms in random constraint satisfaction problems, providing theoretical insights supported by numerical simulations.

Contribution

It introduces a cavity method tailored for partially decimated models, enhancing understanding of message passing algorithms in sparse random graphs.

Findings

The cavity method accurately predicts algorithm performance.

Theoretical results align with extensive numerical simulations.

Insights into the thermodynamics of decimated constraint problems.

Abstract

We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in the particular case of partially decimated random constraint satisfaction problems. This allows to develop a theoretical understanding of a class of algorithms for solving constraint satisfaction problems, in which elementary degrees of freedom are sequentially assigned according to the results of a message passing procedure (belief-propagation). We confront this theoretical analysis to the results of extensive numerical simulations.