Abstract
We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Spanning Out-Tree in the case of directed graphs. The run time of our algorithm is \(O({\it poly}(|V|) + 4^k k^2)\) on undirected graphs, and O(4k |V| ยท|E|) on directed graphs. This improves over the previously fastest algorithms for these problems with run times of \(O({\it poly}(|V|) + 6.75^k {\it poly}(k))\) and \(2^{O(k \log k)} {\it poly}(|V|)\), respectively.
Supported by the DFG under grant RO 927/7-1.
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Kneis, J., Langer, A., Rossmanith, P. (2008). A New Algorithm for Finding Trees with Many Leaves. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_26
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DOI: https://doi.org/10.1007/978-3-540-92182-0_26
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