Abstract
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.
Extended Abstract (Proofs omitted)
Currently on leave from Princeton University. This research is supported by NSF grant MCS80-04490.
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Lieberherr, K.J., Vavasis, S.A. (1982). Analysis of polynomial approximation algorithms for constraint expressions. In: Cremers, A.B., Kriegel, HP. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036480
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DOI: https://doi.org/10.1007/BFb0036480
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