The 2-MAXSAT Problem Can Be Solved in Polynomial Time

04/25/2023

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by   Yangjun Chen, et al.

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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 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 average time complexity is bounded by O(n^3m^3). This shows that the 2-MAXSAT problem can be solved in polynomial time.