Abstract
In this paper we extend recent work about the relationship between the syntactic description of NP optimization problems and their approximation properties. In contrast to Max SNP we consider problems that take arbitrary weighted structures as input instances and we use the framework of Metafinite Model Theory [5] to get a more general definability theory of optimization problems. We define a class MAX φ and show that every problem in this class has a fully polynomial-time approximation scheme (FPTAS), i.e., can be approximated to every desired accuracy ε in time polynomial in the size of the input and 1/ε. An example for a problem in Max φ is Knapsack.
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Malmström, A. (1997). Optimization problems with approximation schemes. In: van Dalen, D., Bezem, M. (eds) Computer Science Logic. CSL 1996. Lecture Notes in Computer Science, vol 1258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63172-0_47
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DOI: https://doi.org/10.1007/3-540-63172-0_47
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