Parameterized edge dominating set in cubic graphs

Authors:
Mingyu Xiao;Hiroshi Nagamochi
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, China;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan
Venue:
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Year:
2011

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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.