A New Empirical Study of Weak Backdoors

Work by Kilby, Slaney, Thiebaux and Walsh [1] showed that the backdoors and backbones of unstructured Random 3SAT instances are largely disjoint. In this work we extend this study to the consideration of backdoors in SAT encodings of structured problems. We show that the results of Kilby et al. also apply to structured problems. Further, we analyse the frequency with which individual variables appear in backdoors for specific problem instances. In all problem classes there are variables with particularly high frequencies of backdoor membership. Backbone variables that do appear in backdoors typically appear in very few.