Abstract
We study the properties of 2-SAT and Max-2-SAT problems by analyzing the node adding process on the factor graph. Two important structures, backbones and mutual-determinations are investigated, and the reduced solution graph for the expression of solution space of 2-SAT and Max-2-SAT is defined. For 2-SAT problem, a complete evolution process for the reduced graph is discussed and corresponding algorithm is obtained. For the Max-2-SAT problem, the analysis shows it’s backbone number can evolve in a much harder way by which it can increase or decrease. The research in this paper provide a new view point for understanding the solution space of 2-SAT and Max-2-SAT, which will be benefit for recognizing the complexity nature of the NP-hard problems.
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