The performance of modern conflict-driven clause learning（CDCL） SAT solvers strongly depends on branching heuristics. State-of-the-art branching heuristics, such as variable state independent decaying sum（VSIDS） and learning rate branching（LRB）, are computed and maintained by aggregating the occurrences of the variables in conflicts. However, these heuristics are not sufficiently accurate at the beginning of the search because they are based on very few conflicts. We propose the distance branching heuristic, which,given a conflict, constructs a complete implication graph and increments the score of a variable considering the longest distance between the variable and the conflict rather than the simple presence of the variable in the graph. We implemented the proposed distance branching heuristic in Maple LCM and Glucose-3.0, two of the best CDCL SAT solvers, and used the resulting solvers to solve instances from the application and crafted tracks of the 2014 and 2016 SAT competitions and the main track of the 2017 SAT competition. The empirical results demonstrate that using the proposed distance branching heuristic in the initialization phase of Maple LCM and Glucose-3.0 solvers improves performance. The Maple LCM solver with the proposed distance branching heuristic in the initialization phase won the main track of the 2017 SAT competition.
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