Polynomial Kernels for Generalized Domination Problems

Pradeesha Ashok; Rajath Rao; Avi Tomar

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arXiv · 2211.03365

Polynomial Kernels for Generalized Domination Problems

Pradeesha Ashok·Rajath Rao·Avi Tomar

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Abstract

In this paper, we study the parameterized complexity of a generalized domination problem called the [${\sigma}, {\rho}$] 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 [${\sigma}, {\rho}$] Dominating Set problem parameterized by treewidth is well studied. Here the properties of the sets ${\sigma}$ and ${\rho}$ that make the problem tractable are identified [1]. We consider a larger parameter and investigate the existence of polynomial sized kernels. When ${\sigma}$ and ${\rho}$ are finite, we identify the exact condition when the [${\sigma}, {\rho}$] 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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Pradeesha Ashok, Rajath Rao, Avi Tomar. 2022-11-07. Polynomial Kernels for Generalized Domination Problems. https://arxiv.org/abs/2211.03365

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