Approximability of the Maximum Solution Problem for Certain Families of Algebras

  • Peter Jonsson
  • Johan Thapper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5675)


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.


Optimisation approximability constraint satisfaction algebra computational complexity 


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Peter Jonsson
    • 1
  • Johan Thapper
    • 1
  1. 1.Department of Computer and Information ScienceLinköpings universitetLinköpingSweden

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