The complexity of selecting maximal solutions

Specific maximization problems, such as the maximal independent set problem and the minimal unsatisfiability problem, are studied in a general framework. The goal is to show what factors make maximization problems hard or easy to solve and how the factors influence the complexity of solving the problems. Maximization problems are divided into several classes, and both upper and lower bounds for them are proved. An important consequence of the results is that finding an X -minimal satisfying truth assignment to a given CNF Boolean formula is complete for NPMV/OptP[O(log n)], solving an open question of C.H. Papadimitriou (1991)