LIPIcs.FSTTCS.2014.85.pdf
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Tree Deletion Set Has a Polynomial Kernel (but no OPT^O(1) Approximation)
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34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2014-12-12
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Archontia C. Giannopoulou, Daniel Lokshtanov, Saket Saurabh, and Ondrej Suchy. Tree Deletion Set Has a Polynomial Kernel (but no OPT^O(1) Approximation). In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 85-96, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.FSTTCS.2014.85
https://doi.org/10.4230/LIPIcs.FSTTCS.2014.85
Abstract
In the Tree Deletion Set problem the input is a graph G together with an integer k. The objective is to determine whether there exists a set S of at most k vertices such that G \ S is a tree. The problem is NP-complete and even NP-hard to approximate within any factor of OPT^c for any constant c. In this paper we give an O(k^5) size kernel for the Tree Deletion Set problem. An appealing feature of our kernelization algorithm is a new reduction rule, based on system of linear equations, that we use to handle the instances on which Tree Deletion Set is hard to approximate.
Keywords
- Tree Deletion Set
- Feedback Vertex Set
- Kernelization
- Linear Equations
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