Abstract
We study the worst-case performance of the maximal matching heuristic applied to the Minimum Vertex Cover and Minimum Maximal Matching problems, through a careful analysis of tight examples. We show that the tight worst-case approximation ratio is asymptotic to \({\rm min}\, \{2, 1/(1-\sqrt{1-\epsilon})\}\) for graphs with an average degree at least εn and to min {2, 1/ε} for graphs with a minimum degree at least εn.
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Cardinal, J., Labbé, M., Langerman, S., Levy, E., Mélot, H. (2005). A Tight Analysis of the Maximal Matching Heuristic. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_71
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DOI: https://doi.org/10.1007/11533719_71
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
Online ISBN: 978-3-540-31806-4
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