Generating hard satisfiable instances by planting into random constraint satisfaction problem model with growing constraint scope length

Abstract

Listen

Translate article

We propose generating hard satisfiable constraint satisfaction problem (CSP) instances by planting into the k-CSP model, which is a random CSP model with growing constraint scope length. The phase diagram of the planted k-CSP model is drawn in this paper, which has no differences from that of the pure random k-CSP model, except that the planted k-CSP model has a planted cluster while the pure random k-CSP model does not. The planted cluster, which is composed of the planted solution and solutions around it, is found to be very small. This phase diagram guarantees that the planted k-CSP instances are as hard as the pure random k-CSP instances before the satisfiability (by configurations outside the planted cluster) transition occurs, and hard satisfiable instances appear near the satisfiable transition point. Experiments on instances with 102 variables support that the model can generate hard satisfiable instances.