An Efficient Fixed-Parameter Enumeration Algorithm for Weighted Edge Dominating Set

Authors:
Jianxin Wang;Beiwei Chen;Qilong Feng;Jianer Chen
Affiliations:
School of Information Science and Engineering, Central South University, Changsha, P.R. China 410083;School of Information Science and Engineering, Central South University, Changsha, P.R. China 410083;School of Information Science and Engineering, Central South University, Changsha, P.R. China 410083;School of Information Science and Engineering, Central South University, Changsha, P.R. China 410083
Venue:
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Year:
2009

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Abstract

Edge Dominating Set problem is an important NP-hard problem. In this paper, we give more detailed structure analysis for the problem, and adopt the enumerate-and-expand technique to construct a fixed-parameter enumeration algorithm. Based on the relationship between Edge Dominating Set and Minimal Vertex Cover, we first find all minimal vertex covers up to 2k size for the instance of problem and then expand these vertex covers with matching property and dynamic programming to get the z smallest k -edge dominating sets. At last, we present an efficient fixed-parameter enumeration algorithm of time complexity O (5.62k k 4 z 2 + 42k nk 3 z ) for the Weighted Edge Dominating Set problem, which is the first result for the enumeration of the Weighted Edge Dominating Set problem.