Abstract
In this paper we initiate a systematic study of the Reduced Degree Spanning Tree ( d -RDST) 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. 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(k 2) vertices on general digraphs. We also give an algorithm for this problem on general digraphs with run-time O *(5.942k). We also consider the dual of d-RDST: given a digraph D and a nonnegative integer k, construct a spanning out-tree of D with at least k vertices of full out-degree. We show that this problem is W[1]-hard on two important digraph classes: directed acyclic graphs and strongly connected digraphs.
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Lokshtanov, D., Raman, V., Saurabh, S., Sikdar, S. (2009). On the Directed Degree-Preserving Spanning Tree Problem. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_23
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DOI: https://doi.org/10.1007/978-3-642-11269-0_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11268-3
Online ISBN: 978-3-642-11269-0
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