Tree Deletion Set Has a Polynomial Kernel (but no OPT^O(1) Approximation)

Authors Archontia C. Giannopoulou, Daniel Lokshtanov, Saket Saurabh, Ondrej Suchy

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Archontia C. Giannopoulou
Daniel Lokshtanov
Saket Saurabh
Ondrej Suchy

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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)


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.
  • Tree Deletion Set
  • Feedback Vertex Set
  • Kernelization
  • Linear Equations


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