Backdoors into Heterogeneous Classes of SAT and CSP

Sebastian Ordyniak

MU Brno

Abstract

Backdoor sets represent clever reasoning shortcuts through the search space for SAT and CSP. By instantiating the backdoor variables one reduces the given instance to several easy instances that belong to a tractable class. The overall time needed to solve the instance is exponential in the size of the backdoor set, hence it is a challenging problem to find a small backdoor set if one exists; over the last years this problem has been subject of intensive research.

In this work we extend the classical notion of a strong backdoor set 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