Abstract
We analyze the simple greedy algorithm that iteratively removes the endpoints of a maximum-degree edge in a graph, where the degree of an edge is the sum of the degrees of its endpoints. This algorithm provides a 2-approximation to the minimum edge dominating set and minimum maximal matching problems. We refine its analysis and give an expression of the approximation ratio that is strictly less than 2 in the cases where the input graph has n vertices and at least \(\epsilon \binom{n}{2}\) edges, for ε> 1/2. This ratio is shown to be asymptotically tight for ε> 1/2.
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Cardinal, J., Langerman, S., Levy, E. (2007). Improved Approximation Bounds for Edge Dominating Set in Dense Graphs. In: Erlebach, T., Kaklamanis, C. (eds) Approximation and Online Algorithms. WAOA 2006. Lecture Notes in Computer Science, vol 4368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11970125_9
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DOI: https://doi.org/10.1007/11970125_9
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