Abstract
We provide the first interesting explicit lower bounds on efficient approximability for two closely related optimization problems in graphs, Minimum Edge Dominating Set and Minimum Maximal Matching. We show that it is NP-hard to approximate the solution of both problems to within any constant factor smaller than \(\frac{7}{6}\). The result extends with negligible loss to bounded degree graphs and to everywhere dense graphs.
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References
Baker, B.S.: Approximation algorithms for NP-complete problems on planar graphs. Journal of ACM 41, 153–180 (1994)
Carr, R., Fujito, T., Konjevod, G., Parekh, O.: A \(2{\frac{1}{10}}\) -approximation algorithm for a generalization of the weighted edge-dominating set problem. Journal of Combinatorial Optimization 5, 317–326 (2001)
Chung, F.R.K.: Spectral Graph Theory. CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence (1997) ISBN 0-8218-0315-8
Chlebík, M., Chlebíková, J.: Approximation hardness for small occurrence instances of NP-hard problems. In: Proc. of the 5th CIAC. LNCS, vol. 2653, pp. 152–164. Springer, Heidelberg (2003) (also ECCC Report TR02-73, 2002)
Chlebík, M., Chlebíková, J.: Inapproximability results for bounded variants of optimization problems. In: Lingas, A., Nilsson, B.J. (eds.) FCT 2003. LNCS, vol. 2751, pp. 27–38. Springer, Heidelberg (2003) (also ECCC Report TR03-26, 2003)
Clementi, A., Trevisan, L.: Improved non-approximability results for vertex cover with density constraints. Theor. Computer Science 225, 113–128 (1999)
Dinur, A., Safra, S.: The importance of being biased, ECCC Report TR02-104 (2001)
Fujito, T., Nagamochi, H.: A 2-approximation algorithm for the minimum weight edge dominating set problem. Discrete Appl. Math. 118, 199–207 (2002)
Håstad, J.: Some optimal inapproximability results. Journal of ACM 48, 798–859 (2001)
Horton, J.D., Kilakos, K.: Minimum edge dominating sets. SIAM J. Discrete Math. 6, 375–387 (1993)
Hunt III, H.B., Marathe, M.V., Radhakrishnan, V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E.: A unified approach to approximation schemes for NP- and PSPACE-hard problems for geometric graphs. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 424–435. Springer, Heidelberg (1994)
Mitchell, S., Hedetniemi, S.: Edge domination in trees. In: Proc. of the 8th Southearn Conf. on Combinatorics, Graph Theory, and Computing, pp. 489–509 (1977)
Srinivasan, A., Madhukar, K., Nagavamsi, P., Pandu Rangan, C., Chang, M.-S.: Edge domination on bipartite permutation graphs and cotriangulated graphs. Inf. Proc. Letters 56, 165–171 (1995)
Yannakakis, M., Gavril, F.: Edge dominating sets in graphs. SIAM J. Appl. Math. 38, 364–372 (1980)
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Chlebík, M., Chlebíková, J. (2003). Approximation Hardness of Minimum Edge Dominating Set and Minimum Maximal Matching. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_43
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DOI: https://doi.org/10.1007/978-3-540-24587-2_43
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