Probabilistic Generalization of Backdoor Trees with Application to SAT

The concept of Strong Backdoor Sets (SBS) for Constraint Satisfaction Problems is well known as one the attempts to exploit structural peculiarities in hard instances. However, practice, finding an SBS a particular instance often harder than solving it. Recently, probabilistic weakened variant was introduced: SBS, all subproblems must be polynomially solvable, whereas only large fraction ρ them should have this property. This new backdoors called ρ-backdoors makes it possible use Monte Carlo method and metaheuristic optimization find with very close 1, relatively fast. Despite fact that ρ-backdoor-based decomposition portion remain, practice narrowing search space allows problem faster such backdoor without In paper, we significantly improve on by extending trees: introduce ρ-backdoor trees, show interconnections between ρ-backdoors, corresponding establish some theoretical properties trees. experimental part moving from trees drastically reducing time required construct decompositions compromising their quality.