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.
This work is supported by the National Natural Science Foundation of China (No. 60773111), the National Grand Fundamental Research 973 Program of China (No. 2008CB317107), the Excellent Youth Foundation of Hunan province of China (No. 06JJ10009), Program for New Century Excellent Talents in University (No. NCET-O5-0683) and Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0661).
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Wang, J., Chen, B., Feng, Q., Chen, J. (2009). An Efficient Fixed-Parameter Enumeration Algorithm for Weighted Edge Dominating Set. In: Deng, X., Hopcroft, J.E., Xue, J. (eds) Frontiers in Algorithmics. FAW 2009. Lecture Notes in Computer Science, vol 5598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02270-8_25
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DOI: https://doi.org/10.1007/978-3-642-02270-8_25
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