eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2014-12-12
85
96
10.4230/LIPIcs.FSTTCS.2014.85
article
Tree Deletion Set Has a Polynomial Kernel (but no OPT^O(1) Approximation)
Giannopoulou, Archontia C.
Lokshtanov, Daniel
Saurabh, Saket
Suchy, Ondrej
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol029-fsttcs2014/LIPIcs.FSTTCS.2014.85/LIPIcs.FSTTCS.2014.85.pdf
Tree Deletion Set
Feedback Vertex Set
Kernelization
Linear Equations