Alimonti P. (1994) New local search approximation techniques for maximum generalized satisfiability problems. In: Bonuccelli M., Crescenzi P., Petreschi R. (eds) Algorithms and Complexity. CIAC 1994. Lecture Notes in Computer Science, vol 778. Springer, Berlin, Heidelberg
We investigate the relationship beetween the classes MAX-NP and GLO by studying the Maximum Generalized Satisfiability problem, which is in the former class. We present a (2−B)-approximate greedy heuristic for this problem and show that no local search c-approximate algorithm exists, based on an h-bounded neighborhood and on the number of satisfied clauses as objective function. This implies that, with the standard definition of local search, MAX-NP is not contained in GLO.
We then show that, by introducing a different local search technique, that is using a different neighborhood structure for B = 2 and an auxiliary objective function in the general case, a local search (2−B)-approximate algorithms can be found for this problem. The latter result, that holds in the general case, suggests how to modify the definition of local search in order to extend the power of this general approch. In the same way, we can enlarge the class GLO of problems that can be efficiently approximated by local search techniques.