Backdoors into Heterogeneous Classes of SAT and CSP

TL;DR

This paper extends the concept of backdoor sets in SAT and CSP to heterogeneous base classes, providing a detailed complexity analysis of detecting such backdoors, which can be smaller and more desirable than homogeneous ones.

Contribution

It introduces the notion of heterogeneous backdoor sets for SAT and CSP and analyzes their computational complexity in detail.

Findings

Heterogeneous backdoor sets can be significantly smaller than homogeneous ones.

The paper provides a comprehensive complexity landscape for detecting these backdoors.

Heterogeneous backdoors are potentially more practical for solving SAT and CSP instances.

Abstract

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.