Backdoors into Heterogeneous Classes of SAT and CSP
This work addresses computational complexity challenges in constraint satisfaction for researchers in theoretical computer science, but it appears incremental as it builds on classical notions.
The paper tackles the problem of extending backdoor sets for SAT and CSP to heterogeneous base classes, which can be smaller but harder to find, and provides a detailed complexity analysis for detecting these sets.
In this paper we extend the classical notion of strong and weak backdoor sets for SAT and CSP by allowing that different instantiations of the backdoor variables result in instances that belong to different base classes; the union of the base classes forms a heterogeneous base class. Backdoor sets to heterogeneous base classes can be much smaller than backdoor sets to homogeneous ones, hence they are much more desirable but possibly harder to find. We draw a detailed complexity landscape for the problem of detecting strong and weak backdoor sets into heterogeneous base classes for SAT and CSP.