# Upper and Lower Bounds for Weak Backdoor Set Detection

arXiv: https://arxiv.org/abs/1304.5518 · HTML: https://mlsanity.com/paper/1304.5518/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2013.

## Built on by (most cited first, 1 of 1)

- [Decomposing Hard SAT Instances with Metaheuristic Optimization](https://mlsanity.com/paper/2312.10436/) (2023)

## Abstract (arXiv)

We obtain upper and lower bounds for running times of exponential time algorithms for the detection of weak backdoor sets of 3CNF formulas, considering various base classes. These results include (omitting polynomial factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas. These bounds improve an earlier known bound of 6^k. We also prove a 2^k lower bound for these problems, subject to the Strong Exponential Time Hypothesis.