The maximum satisfiability problem (Max-Sat) is the problem of finding the maximum number of clauses that can be satisified in a Boolean satisfiability instance. The exactly 1 in 2 Sat problem asks, given a set of clauses each with two literals, is there a set of literals such that each clause has exactly one literal from this set.
The Complexity of Making Unique Choices: Approximating 1-in-k SAT by Guruswami and Trevisan gives a method for approximating Max 1 in 2 Sat. They state monotone (no negated literals) Max 1 in 2 Sat "admits an e-approximation in polynomial time".
I would like to find an exact algorithm for the Max monotone 1 in 2 Sat problem.