The 2-MAXSAT Problem Can Be Solved in Polynomial Time

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 an efficient algorithm to solve this problem. Its worst case time complexity is bounded by O($(nm)^2(log_2\;nm)^{log_2\;nm}$). This shows that the 2-MAXSAT problem can be solved in polynomial time.