Parameterizing MAX SNP problems above guaranteed values

Authors:
Meena Mahajan;Venkatesh Raman;Somnath Sikdar
Affiliations:
The Institute of Mathematical Sciences, Chennai;The Institute of Mathematical Sciences, Chennai;The Institute of Mathematical Sciences, Chennai
Venue:
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Year:
2006

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Abstract

We show that every problem in MAX SNP has a lower bound on the optimum solution size that is unbounded and that the above guarantee question with respect to this lower bound is fixed parameter tractable. We next introduce the notion of “tight” upper and lower bounds for the optimum solution and show that the parameterized version of a variant of the above guarantee question with respect to the tight lower bound cannot be fixed parameter tractable unless P = NP, for a class of NP-optimization problems.