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http://dx.doi.org/10.7236/JIIBC.2022.22.5.1

Algorithm for Minimum Degree Inter-vertex Edge Selection of Maximum Matching Problem  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.22, no.5, 2022 , pp. 1-6 More about this Journal
Abstract
This paper deals with the maximum cardinality matching(MCM) problem. The augmenting path technique is well known in MCM. MCM is obtained by $O({\sqrt{n}}m)$ time complexity augmenting path algorithm for the general graph, and O(m log n) algorithm for the bipartite graph. On the other hand, this paper suggests O(n) linear time algorithm. The proposed algorithm based on the basic principle of as possible as largest selected inter-vertex edges in order to obtain the MCM. This paper simply selects edge {u,𝜐} that the minimum degree vertex u and minimum degree vertex 𝜐 in NG(u) 𝜈(G)=k times iteration. For various general and bipartite graphs experimental data, this algorithm can be get the 𝜈(G) exactly.
Keywords
Maximum cardinality matching; Maximal; Maximum; minimum degree; Neighborhood;
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1 V. V. Vazirani, "A Simplification of the MV Matching Algorithm and its Proof," Cornell University Library, pp. 1-32, Aug. 2013, CoRR abs/1210.4594, arXiv:1210.4594
2 Z. Galil, " Efficient Algorithms for Finding Maximum Matching in Graphs," ACM Computing Surveys, Vol. 18, No. 1, pp. 23-38, Mar. 1988, https://doi.org/10.1145/6462.6502   DOI
3 A. Quattoni, X. Carreras, and M. Galle, "A Maximum Matching Algorithm for Basis Selection in Spectral Learning," Cornell University Library, pp. 1-13, Jun. 2017, arXiv:1706.02857
4 S. Micali and V. V. Vazirani, "An O($\sqrt[]{n}$m)Algorithm for Finding Maximum Matching in General Graphs," Proceedings of 21st IEEE Symposium on Foundations of Computer Science, pp. 17-27, Oct. 1980, https://doi.org/10.1109/ SFCS.1980.12.   DOI
5 J. E. Hopcroft and R. M. Karp, "An n5/2 Algorithm for Maximum Matchings in Bipartite Graphs," SIAM Journal on Computing, Vol. 2, No. 4, pp. 225-231, Dec. 1973, https://doi.org/10.1137/0202019.   DOI
6 O. Giel and I. Wegener, "Evolutionary Algorithms and the Maximum Matching Problem," Annual Symposium on Theoretical Aspects of Computer Science, pp. 415-426, Feb. 2003, https://doi.org/ 10.1007/ 3-540-36494-3_37   DOI
7 J. He and X. Tao, "Time Complexity Analysis of an Evolutionary Algorithm for Finding Nearly Maximum Cardinality Matching," Journal of Computer Science and Technology, Vol. 19, No. 4, pp. 450-458, Jul. 2004, https://doi.org/10.1007/BF02944746   DOI
8 V. M Shettar and S. A. Angadi, "A Genetic Algorithm for Graph Matching Using Graph Node Characteristics," Journal of Mathematical Sciences International Research, Vol. 4, No. 2, pp. 347-351, 2015, ISBN:978-93-84124-53-3
9 N. Blum, "A New Approach to Maximum Matching in General Graphs," International Colloquium on Automata, Languages, and Programming, pp. 586-597, 1990, https://doi.org/10.1007/BFb0032060   DOI
10 T. Kameda and I. Munro, "A O(IVI IEI) Algorithm for Maximum Matching of Graphs," Computing, Vol. 12, No. 1, pp. 91-98, Mar. 1974, https://doi.org/10.1007/BF02239502   DOI
11 C. Witzgall and C. T. Zahn, "Modification of Edmonds' Maximum Matching Algorithm" Journal of Research of the National Bureou of Standards, Vol. 69B, No. 1-2, Jan. 1965,
12 O. Chaleb, " Introduction to Maximum Matching in Graphs," http://people.scs.carleton.ca/~maheshwa/ courses/5703COMP/16Fall/Matching-Report.pdf, 2016.