MAXIMUM 2-SATISFIABILITY is approximable within 1.0741 [143], and is not approximable within 1.0476 [226]. The weighted version of this problem is as hard to approximate as the unweighted version [120].
If every clause consists of exactly k literals, the weighted version of
the problem is as hard to approximate as the unweighted version
[120].
Variation in which the number of occurrences of any literal is
bounded by a constant B for
is still APX-complete
[371] and [42];
for B=6 it is not approximable within 1.0014 [70].
Admits a PTAS if
[37].
Variation in which each clause is a Horn clause, i.e., contains at most
one nonnegated variable, is APX-complete, even for k=2 [311].