Solving the 2-MAXSAT Problem in Polynomial Time: a Proof of $\textit{P}$ = $\textit{NP}$

Abstract: 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 $\textit{NP}$-complete even for its restricted version, the 2-MAXSAT problem by which every clause contains at most 2 literals. In this paper, we discuss an efficient algorithm to solve this problem. Its worst-case time complexity is bounded by O($n^2m^4$). This shows that the 2-MAXSAT problem can be solved in polynomial time. Thus, the paper in fact provides a proof of $P$ = $\textit{NP}$.