# Combining Treewidth and Backdoors for CSP

arXiv: https://arxiv.org/abs/1610.03298 · HTML: https://mlsanity.com/paper/1610.03298/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2016.

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

- [Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs](https://mlsanity.com/paper/2108.03022/) (2021)
- [Solving Projected Model Counting by Utilizing Treewidth and its Limits](https://mlsanity.com/paper/2305.19212/) (2023)

## Abstract (arXiv)

We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability for CSP: (i) by structural restrictions on the interaction between the variables and the constraints and (ii) by language restrictions on the relations that can be used inside the constraints. Apart from defining the notion of backdoor-treewidth and showing how backdoors of small treewidth can be used to efficiently solve CSP, our main technical contribution is a fixed-parameter algorithm that finds a backdoor of small treewidth.