Parametric Duality: Kernel Sizes and Algorithmics

We derive certain properties for problems which are parameterized tractable both in their \primal" and in their \dual" parameterization. In particular, we derive the rst ever lower bounds result for kernel sizes of parameterized problems. We discuss various consequences of this result. Moreover, we explain how to get improved non-parameterized algorithms from known parameterized algorithms by a \two-side attack."

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