Research map / Learning theory and algorithms / Combinatorial and search optimization
On Probabilistic Generalization of Backdoors in Boolean Satisfiability
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a found ρ-backdoor to decompose the instance before SAT solving | SAT solvers on the reported hard CNF instances · PvS4,7; BvP4,8; BvP6,7; pmg12; sgen150; PHP13,12; PHP15,14 | decomposition rate: 0.30; 0.77; 0.69; 0.23; 0.25; 0.34; 0.91 | Helped |
| Use several found ρ-backdoors simultaneously instead of an individual backdoor | SAT solving with ρ-backdoors · PvS4,7 | decomposition rate: 0.06 | Helped |
| Use four combined ρ-backdoors | Glucose 3.0 and Glucose 4.1 · pmg12 | decomposition rate: < 0.01; < 0.1 | Helped |
| Use the genetic algorithm rather than (1+1)-EA to search for backdoors (ablation) | PvS4,7 backdoor search · PvS4,7 | decomposition rate | Helped |
| Start the search from an empty backdoor rather than the full variable set (ablation) | Metaheuristic ρ-backdoor search · SAT instances | backdoor quality | Mixed |
| Use the Monte Carlo estimate of ρ instead of checking every assignment | Probabilistic backdoor evaluation · CNF formulas | evaluation cost: poly(|C|) · 16·ln(2/δ)/ε² | Helped |
| Use the proposed minimum (ε, δ)-SBS search instead of exhaustive minimum-SBS search | Minimum backdoor search · CNF formulas | worst-case complexity: O(p(|C|) · k · 16·ln(2/δ)/ε² · 2^|X|) versus O(p(|C|) · 3^|X|) | Helped |
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