Approximability of the Maximum Solution Problem for Certain Families of Algebras

Authors:
Peter Jonsson;Johan Thapper
Affiliations:
Department of Computer and Information Science, Linköpings universitet, Linköping, Sweden SE-581 83;Department of Computer and Information Science, Linköpings universitet, Linköping, Sweden SE-581 83
Venue:
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Year:
2009

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Abstract

We study the approximability of the maximum solution problem . This problem is an optimisation variant of the constraint satisfaction problem and it captures a wide range of interesting problems in, for example, integer programming, equation solving, and graph theory. The approximability of this problem has previously been studied in the two-element case [Khanna et al, `The approximability of constraint satisfaction', SIAM Journal on Computing 23(6), 2000] and in some algebraically motivated cases [Jonsson et al, `Max Ones generalized to larger domains', SIAM Journal on Computing 38(1), 2008]. We continue this line of research by considering the approximability of Max Sol for different types of constraints. Our investigation combined with the older results strengthens the hypothesis that Max Sol exhibits a pentachotomy with respect to approximability.