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

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.Comment: 32 pages, 24 figure

The condensation phase transition in the regular kk-SAT model

Much of the recent work on random constraint satisfaction problems has been inspired by ingenious but non-rigorous approaches from physics. The physics predictions typically come in the form of distributional fixed point problems that are intended to mimic Belief Propagation, a message passing algorithm, applied to the random CSP. In this paper we propose a novel method for harnessing Belief Propagation directly to obtain a rigorous proof of such a prediction, namely the existence and location of a condensation phase transition in the random regular $k$-SAT model.Comment: Revised version based on arXiv:1504.03975, version

Robust Mission Design Through Evidence Theory and Multi-Agent Collaborative Search

In this paper, the preliminary design of a space mission is approached introducing uncertainties on the design parameters and formulating the resulting reliable design problem as a multiobjective optimization problem. Uncertainties are modelled through evidence theory and the belief, or credibility, in the successful achievement of mission goals is maximised along with the reliability of constraint satisfaction. The multiobjective optimisation problem is solved through a novel algorithm based on the collaboration of a population of agents in search for the set of highly reliable solutions. Two typical problems in mission analysis are used to illustrate the proposed methodology

Finite Energy Survey Propagation for Constraint Satisfaction Problems

The Survey Propagation (SP) algorithm [1] has recently been shown to work well in the hard region for random K-SAT problems. SP has its origins in sophisticated arguments in statistical physics, and can be derived from an approach known as the cavity method, when applied at what is called the one-step replica symmetry breaking level. In its most general form, SP can be applied to general constraint satisfaction problems, and can also be used in the unsatisfiable region, where the aim is to minimize the number of violated constraints. In this paper, we formulate the SP-Y algorithm for general constraint satisfaction problems, applicable for minimizing the number of violated constraints. This could be useful, for example, in solving approximate subgraph isomorphism problems. Preliminary results show that SP can solve a few instances of induced subgraph isomorphism for which belief propagation failed to converge.Singapore-MIT Alliance (SMA