---
title: 'A Fixed-Parameter Algorithm for #SAT with Parameter Incidence Treewidth'
url: https://www.emergentmind.com/papers/0610174
type: paper
arxiv_id: '0610174'
arxiv_url: https://arxiv.org/abs/0610174
published: '2006-10-31'
categories:
- cs.DS
- cs.CC
- cs.LO
---

# A Fixed-Parameter Algorithm for #SAT with Parameter Incidence Treewidth

## Abstract

We present an efficient fixed-parameter algorithm for #SAT parameterized by the incidence treewidth, i.e., the treewidth of the bipartite graph whose vertices are the variables and clauses of the given CNF formula; a variable and a clause are joined by an edge if and only if the variable occurs in the clause. Our algorithm runs in time O(4^k k l N), where k denotes the incidence treewidth, l denotes the size of a largest clause, and N denotes the number of nodes of the tree-decomposition.