Polynomial Kernels for Generalized Domination Problems
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In this paper, we study the parameterized complexity of a generalized domination problem called the [σ, ρ] Dominating Set problem. This problem generalizes a large number of problems including the Minimum Dominating Set problem and its many variants. The parameterized complexity of the [σ, ρ] Dominating Set problem parameterized by treewidth is well studied. Here the properties of the sets σ and ρ that make the problem tractable are identified [1]. We consider a larger parameter and investigate the existence of polynomial sized kernels. When σ and ρ are finite, we identify the exact condition when the [σ, ρ] Dominating Set problem parameterized by vertex cover admits polynomial kernels. Our lower and upper bound results can also be extended to more general conditions and provably smaller parameters as well.
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