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Lossy Kernels for Hitting Subgraphs

Authors Eduard Eiben, Danny Hermelin, M. S. Ramanujan

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Eduard Eiben
Danny Hermelin
M. S. Ramanujan

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Eduard Eiben, Danny Hermelin, and M. S. Ramanujan. Lossy Kernels for Hitting Subgraphs. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.MFCS.2017.67

Abstract

In this paper, we study the Connected H-hitting Set and Dominating Set problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the Connected H-hitting set problem, we obtain an \alpha-approximate kernel for every \alpha>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the Dominating Set problem on d-degenerate graphs and provide an interpolation of approximate kernels between the known d^2-approximate kernel of constant size and 1-approximate kernel of size k^{O(d^2)}.

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Keywords
  • parameterized algorithms
  • lossy kernelization
  • graph theory

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