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IWPEC

2009

Springer

2009

Springer

In this paper we initiate a systematic study of the Reduced Degree Spanning Tree problem, where given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree with at most k vertices of reduced out-degree. This problem is a directed analog of the wellstudied Minimum-Vertex Feedback Edge Set problem. We show that this problem is ﬁxed-parameter tractable and admits a problem kernel with at most 8k vertices on strongly connected digraphs and O(k2 ) vertices on general digraphs. We also give an algorithm for this problem on general digraphs with runtime O∗ (5.942k ). This adds the Reduced Degree Spanning Tree problem to the small list of directed graph problems for which ﬁxed-parameter tractable algorithms are known. Finally, we consider the dual of Reduced Degree Spanning Tree, that is, given a digraph D and a nonnegative integer k, the goal is to construct a spanning out-tree of D with at least k vertices of full out-degree. We show that this problem is...

Related Content

Added |
27 May 2010 |

Updated |
27 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
IWPEC |

Authors |
Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh, Somnath Sikdar |

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