Abstract
Chen and Kanj considered the Vertex Cover problem for graphs with perfect matchings (VC-PM). They showed that: (i) There is a reduction from general Vertex Cover to VC-PM, which guarantees that if one can achieve an approximation factor of less than two for VC-PM, then one can do so for general Vertex Cover as well. (ii) There is an algorithm for VC-PM whose approximation factor is given as \(1.069+0.069\overline{d}\) where \(\overline{d}\) is the average degree of the given graph. In this paper we improve (ii). Namely we give a new VC-PM algorithm which greatly outperforms the above one and its approximation factor is roughly \(2-\frac{6.74}{\overline{d} + 6.28}\). Our algorithm also works for graphs with “large” matchings although its approximation factor is degenerated.
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Imamura, T., Iwama, K., Tsukiji, T. (2004). Approximated Vertex Cover for Graphs with Perfect Matchings. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_16
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DOI: https://doi.org/10.1007/978-3-540-27798-9_16
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