# Backdoors into Heterogeneous Classes of SAT and CSP

arXiv: https://arxiv.org/abs/1509.05725 · HTML: https://mlsanity.com/paper/1509.05725/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [Learning Small Decision Trees with Few Outliers: A Parameterized Perspective](https://mlsanity.com/paper/2505.15648/) (2025)
- [Computational Short Cuts in Infinite Domain Constraint Satisfaction](https://mlsanity.com/paper/2211.10144/) (2022)

## Abstract (arXiv)

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.