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By the MAXSAT problem, we are given a set $V$ of $m$ variables and acollection $C$ of $n$ clauses over $V$. We will seek a truth assignment tomaximize the number of satisfied clauses. This problem is $\textit{NP}$-hardeven for its restricted version, the 2-MAXSAT problem by which every clausecontains at most 2 literals. In this paper, we discuss an efficient algorithmto solve this problem. Its average time complexity is bounded by O($n^3m^3).This shows that the 2-MAXSAT problem can be solved in polynomial time.

The 2-MAXSAT Problem Can Be Solved in Polynomial Time