By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$. We will seek a truth assignment to maximize the number of satisfied clauses. This problem is $\textit{NP}$-hard even for its restricted version, the 2-MAXSAT problem by which every clause contains at most 2 literals. In this paper, we discuss a polynomial time algorithm to solve this problem. Its time complexity is bounded by O($n^2m^3$). So we believe that $\textit{P}$ = $\textit{NP}$.
翻译:在MAXSAT问题中,我们给定一组包含m个变量的集合V,以及由n个子句构成的集合C(子句均定义于V上)。目标是寻找一个真值赋值,使得满足的子句数量最大化。该问题的限制版本——2-MAXSAT问题(其中每个子句至多包含2个文字)——已被证明是$\textit{NP}$-难的。本文讨论了一种用于求解该问题的多项式时间算法,其时间复杂度上界为O($n^2m^3$)。据此,我们认为$\textit{P}$ = $\textit{NP}$。