Analysis of polynomial approximation algorithms for constraint expressions
The generalized maximum satisfiability problem contains a large class of interesting combinatorial optimization problems. Since most of them are NP-complete we analyze fast approximation algorithms.
Every generalized ψ-satisfiability problem has a polynomial ɛψ-approximate algorithm for a naturally defined constant ɛψ, 0≤ɛψ>1 which is determined here explicitly for several ψ. It is shown that ɛψ can be approximated by the Soviet Ellipsoid Algorithm. The fraction ɛψis known to be best-possible in the sense that the following set is NP-complete: The ψ-formulas S which have an assignment satisfying the fraction τ' <1−ɛψ(τ' rational) of all clauses in S.
Among other results we also show that for many ψ, local search algorithms fail to be ɛψ-approximate algorithms. In some cases, local search algorithms can be arbitrarily far from optimal.
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