Abstract
An induced matching is a matching in which each two edges of the matching are not connected by a joint edge. Induced matchings are well-studied combinatorial objects and a lot of consideration has been given to finding maximum induced matchings, which is an NP-complete problem. Specifically, finding maximum induced matchings in regular graphs is well-known to be NP-complete. A couple of papers lately showed a couple of simple greedy algorithm that approximate a maximum induced matching with a factor of \(d - {\frac{1}{2}}\) and d − 1 (different papers – different factors), where d is the degree of regularity. We show here a simple algorithm with an 0.75d + 0.15 approximation factor. The algorithm is simple – the analysis is not.
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References
Cameron, K.: Induced matchings. Discrete Applied Mathematics 24, 97–102 (1989)
Cameron, K.: Induced matchings in intersection graphs. In: Proceedings of the Sixth International Conference on Graph Theory, Marseille, France (August 2000)
Duckworth, W., Manlove, D., Zito, M.: On the approximability of the maximum induced matching problem. Journal of Discrete Algorithms 3(1), 79–91 (2005)
Erdos, P.: Problems and results in combinatorial analysis and graph theory. Discrete Mathematics 72, 81–92 (1988)
Faudree, R.J., Gyarfas, A., Schelp, R.H., Tuza, Z.: Induced matchings in bipartite graphs. Discrete Mathematics 78, 83–87 (1989)
Fricke, G., Lasker, R.: Strong matchings in trees. Congressus Numerantium 89, 239–244 (1992)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1980)
Golumbic, M.C., Laskar, R.C.: Irredundancy in circular arc graphs. Discrete Applied Mathematics 44, 79–89 (1993)
Golumbic, M.C., Lewenstein, M.: New results on induced matchings. Discrete Applied Mathematics 101, 157–165 (2000)
Horak, P., Qing, H., Trotter, W.T.: Induced matchings in cubic graphs. Journal of Graph Theory 17(2), 151–160 (1993)
Ko, C.W., Shepherd, F.B.: Adding an identity to a totally unimodular matrix. Working paper LSEOR.94.14, London School of Economics, Operational Research Group (1994)
Steger, A., Yu, M.: On induced matchings. Discrete Mathematics 120, 291–295 (1993)
Stockmeyer, L.J., Vazirani, V.V.: NP-completeness of some generalization of the maximum matching problem. Information Processing Letters 15(1), 14–19 (1982)
Zito, M.: Induced matchings in regular graphs and trees. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 89–100. Springer, Heidelberg (1999)
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Gotthilf, Z., Lewenstein, M. (2006). Tighter Approximations for Maximum Induced Matchings in Regular Graphs. In: Erlebach, T., Persinao, G. (eds) Approximation and Online Algorithms. WAOA 2005. Lecture Notes in Computer Science, vol 3879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671411_21
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DOI: https://doi.org/10.1007/11671411_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32207-8
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