Towards a Unified Solution for Constraint-Satisfaction Problems: A Survey-Propagation Approach Based on Normal Realizations

Motivated by the celebrated success of survey propagation (SP) in solving k-SAT problems and its recent applications in coding and data compression, this paper approaches general constraint satisfaction problems from a unified perspective, aiming at developing a general SP-style algorithmic framework for such problems. Although many aspects along our direction remain open, in this paper, we have arrived at a unified combinatorial framework, "lifting" the solution space to what we call the space of all "rectangles". We also present a Markov random field (MRP) formalism over this space using a normal realization. This MRP formalism then brings to surface a new SP-style algorithm family, which contains the existing SP algorithms as a special case