A Hypergraph Container Method on Spread SAT: Approximation and Speedup

Authors: Zicheng Han, Yupeng Lin, Jie Ma, Xiande Zhang

We develop a hypergraph container method for the Boolean Satisfiability Problem (SAT) via the newly developed container results [Campos and Samotij (2024)]. This provides an explicit connection between the extent of spread of clauses and the efficiency of container-based algorithms. Informally, the more evenly the clauses are distributed, the stronger the shrinking effect of the containers, which leads to faster algorithms for SAT. To quantify the extent of spread, we use a weighted point of view, in which a clause of size $s$ receives weight $p^s$ for some $0