A backbone-search heuristic for efficient solving of hard 3-SAT formulae

Of late, new insight into the study of random k-SAT formulae has been gained from the introduction of a concept inspired by models of physics, the ‘backbone’ of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number of clauses. In the present paper, we show that this concept, already invaluable from a theoretical viewpoint in the study of the satisfiability transition, can also play an important role in the design of efficient DPL-type algorithms for solving hard random k-SAT formulae and more specifically 3-SAT formulae. We define a heuristic search for variables belonging to the backbone of a 3-SAT formula which are chosen as branch nodes for the tree developed by a DPL-type procedure. We give in addition a simple technique to magnify the effect of the heuristic. Implementation yields DPL-type algorithms with a significant performance improvement over the best current algorithms, making it possible to handle unsatisfiable hard 3-SAT formulae up to 700 variables.