Bounds for Random Constraint Satisfaction Problems via Spatial Coupling

We report on a novel technique called spatial coupling and its application in the analysis of random constraint satisfaction problems (CSP). Spatial coupling was invented as an engineering construction in the area of error correcting codes where it has resulted in efficient capacity-achieving codes for a wide range of channels. However, this technique is not limited to problems in communications, and can be applied in the much broader context of graphical models. We describe here a general methodology for applying spatial coupling to random constraint satisfaction problems and obtain lower bounds for their (rough) satisfiability threshold. The main idea is to construct a distribution of geometrically structured random K-SAT instances - namely the spatially coupled ensemble - which has the same (rough) satisfiability threshold, and is at the same time algorithmically easier to solve. Then by running well-known algorithms on the spatially coupled ensemble we obtain a lower bound on th...

• Type: Journal
• Year: 2016
• Where: SODA
• Authors: Dimitris Achlioptas, Seyed Hamed Hassani, Nicolas Macris, Rüdiger L. Urbanke
• Keywords: Algorithms, SODA 2016