Abstract
The ROOTED MAXIMUM LEAF OUTBRANCHING problem consists in finding a spanning directed tree rooted at some prescribed vertex of a digraph with the maximum number of leaves. Its parameterized version asks if there exists such a tree with at least k leaves. We use the notion of s − t numbering studied in [19,6,20] to exhibit combinatorial bounds on the existence of spanning directed trees with many leaves. These combinatorial bounds allow us to produce a constant factor approximation algorithm for finding directed trees with many leaves, whereas the best known approximation algorithm has a \(\sqrt{OPT}\)-factor [11]. We also show that ROOTED MAXIMUM LEAF OUTBRANCHING admits an edge-quadratic kernel, improving over the vertex-cubic kernel given by Fernau et al [13].
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Daligault, J., Thomassé, S. (2009). On Finding Directed Trees with Many Leaves. 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_7
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DOI: https://doi.org/10.1007/978-3-642-11269-0_7
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