Algorithms for variable-weighted 2-SAT and dual problems

In this paper we study NP-hard variable-weighted satisfiability optimization problems for the class 2-CNF providing worst-case upper time bounds holding for arbitrary real-valued weights. Moreover, we consider the monotone dual class consisting of clause Sets where all variables occur at most twice. We show that weighted SAT, XSAT and NAESAT optimization problems for this class are polynomial time solvable using appropriate reductions to specific polynomial time solvable graph problems.