LIPIcs.IPEC.2015.199.pdf
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Linear Kernels for Outbranching Problems in Sparse Digraphs
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10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Parameterized and Exact Computation (IPEC) - License:
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- Publication Date: 2015-11-19
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Marthe Bonamy, Lukasz Kowalik, Michal Pilipczuk, and Arkadiusz Socala. Linear Kernels for Outbranching Problems in Sparse Digraphs. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 199-211, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.IPEC.2015.199
https://doi.org/10.4230/LIPIcs.IPEC.2015.199
Abstract
In the k-Leaf Out-Branching and k-Internal Out-Branching problems we are given a directed graph D with a designated root r and a nonnegative integer k. The question is to determine the existence of an outbranching rooted at r that has at least k leaves, or at least k internal vertices, respectively. Both these problems were intensively studied from the points of view of parameterized complexity and kernelization, and in particular for both of them kernels with O(k^2) vertices are known on general graphs. In this work we show that k-Leaf Out-Branching admits a kernel with O(k) vertices on H-minor-free graphs, for any fixed H, whereas k-Internal Out-Branching admits a kernel with O(k) vertices on any graph class of bounded expansion.
Keywords
- FPT algorithm
- kernelization
- outbranching
- sparse graphs
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References
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