Tradeoffs in the Complexity of Backdoor Detection

Abstract There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them. Some of these properties are “easily” identifiable, while others such as backdoor sets are of interest because they capture key aspects of state-of-the-art constraint solvers as well as of many real-world problem instances. In particular, it was recently shown that the problem of identifying a strong Horn- or 2CNF-backdoor can be solved by exploiting equivalence with deletion backdoors, and is NP-complete. We prove that strong backdoor identification becomes harder than NP (unless NP=coNP) as soon as the inconsequential sounding feature of empty clause detection (present in all modern SAT solvers) is added. More interestingly, in practice such a feature as well as polynomial time constraint propagation mechanisms often lead to much smaller backdoor sets. We show experimentally that instances from real-world do...

• Type: Conference
• Year: 2007
• Where: CP
• Authors: Bistra N. Dilkina, Carla P. Gomes, Ashish Sabharwal
• Keywords: Backdoor Sets, CP 2007, Programming Languages, Strong Backdoor Identification, Strong Backdoors