An Improved Algorithm for Sparse Instances of SAT
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909385781936128 |
|---|---|
| author | Jain, Sanjay Neoh, Tzeh Yuan Stephan, Frank |
| author_facet | Jain, Sanjay Neoh, Tzeh Yuan Stephan, Frank |
| contents | We show that the CNF satisfiability problem (SAT) can be solved in time $O^*(1.1199^{(d-2)n})$, where $d$ is either the maximum number of occurrences of any variable or the average number of occurrences of all variables if no variable occurs only once. This improves upon the known upper bound of $O^*(1.1279^{(d-2)n})$ by Wahlstr$\ddot{\text{o}}$m (SAT 2005) and $O^*(1.1238^{(d-2)n})$ by Peng and Xiao (IJCAI 2023). For $d\leq 4$, our algorithm is better than previous results. Our main technical result is an algorithm that runs in $O^*(1.1199^n)$ for 3-occur-SAT, a restricted instance of SAT where all variables have at most 3 occurrences. Through deeper case analysis and a reduction rule that allows us to resolve many variables under a relatively broad criteria, we are able to circumvent the bottlenecks in previous algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Improved Algorithm for Sparse Instances of SAT Jain, Sanjay Neoh, Tzeh Yuan Stephan, Frank Data Structures and Algorithms We show that the CNF satisfiability problem (SAT) can be solved in time $O^*(1.1199^{(d-2)n})$, where $d$ is either the maximum number of occurrences of any variable or the average number of occurrences of all variables if no variable occurs only once. This improves upon the known upper bound of $O^*(1.1279^{(d-2)n})$ by Wahlstr$\ddot{\text{o}}$m (SAT 2005) and $O^*(1.1238^{(d-2)n})$ by Peng and Xiao (IJCAI 2023). For $d\leq 4$, our algorithm is better than previous results. Our main technical result is an algorithm that runs in $O^*(1.1199^n)$ for 3-occur-SAT, a restricted instance of SAT where all variables have at most 3 occurrences. Through deeper case analysis and a reduction rule that allows us to resolve many variables under a relatively broad criteria, we are able to circumvent the bottlenecks in previous algorithms. |
| title | An Improved Algorithm for Sparse Instances of SAT |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2411.07389 |