Minimum Weighted Maximal Matching Problem in Trees

Date

2015-06-21

Author

Tural, Mustafa Kemal

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Given a weighted simple graph, the minimum weighted maximal matching (MWMM) problem is the problem of finding a maximal matching of minimum weight. The MWMM problem is NP-hard in general, but is polynomial-time solvable in some special classes of graphs. For instance, it has been shown that the MWMM problem can be solved in linear time in trees when all the edge weights are equal to one. We show that the convex hull of the incidence vectors of maximal matchings (i.e., the maximal matching polytope) in trees is given by the polyhedron described by the linear programming relaxation of a recently proposed integer programming formulation. This establishes the polynomial-time solvability of the MWMM problem in weighted trees. The question of whether or not the MWMM problem can be solved in linear time in weighted trees in open.

URI

http://s3-eu-west-1.amazonaws.com/kg15/production/news/5_book_of_abstracts.pdf?1434179614
https://hdl.handle.net/11511/73200

Conference Name

8th Slovenian Conference on Graph Theory, (21-27 Haziran 2015)

Collections

Department of Industrial Engineering, Conference / Seminar

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Citation Formats

M. K. Tural, “Minimum Weighted Maximal Matching Problem in Trees,” presented at the 8th Slovenian Conference on Graph Theory, (21-27 Haziran 2015), Kranjska Gora, Slovenya, 2015, Accessed: 00, 2021. [Online]. Available: http://s3-eu-west-1.amazonaws.com/kg15/production/news/5_book_of_abstracts.pdf?1434179614.