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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6681))

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Abstract

In this paper, we present an improved algorithm to decide whether a graph of maximum degree 3 has an edge dominating set of size at most k or not, which is based on enumeration of vertex covers. We first enumerate vertex covers of size at most 2k and then construct an edge dominating set based on each vertex cover to find a satisfied edge dominating set. To enumerate vertex covers, we use a branch-and-reduce method that will generate a search tree of size O(2.1479k). Then we get the running time bound of the algorithm.

The work is supported in part by National Natural Science Foundation of China Grant No. 60903007.

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Xiao, M., Nagamochi, H. (2011). Parameterized Edge Dominating Set in Cubic Graphs. In: Atallah, M., Li, XY., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 6681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21204-8_14

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  • DOI: https://doi.org/10.1007/978-3-642-21204-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21203-1

  • Online ISBN: 978-3-642-21204-8

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