CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 5, No 4 (2019): CAUCHY

Problem of Maximum Matching in Non-Bipartite Graph Using Edmonds’ Cardinality Matching Algorithm and Its Applicationin the Battle of Britain Case

Abrori, Muchammad (Unknown)
Jauhari, Mohammad Imam (Unknown)



Article Info

Publish Date
17 Jun 2019

Abstract

Matching is a part of graph theory that discusses pair. A matching M is called to be maximum if M has the highest number of  elements. A blossom which is encountered in non-bipartite graph can cause failure in process of finding the maximum matching in non-bipartite graph. One of the algorithms that can be used to find a maximum matching in non-bipartite graph is Edmonds’ Cardinality Matching Algorithm. Shrinking process is done in each blossom Bi that is encountered to become pseudovertex bi, in a way that each blossom does not interfere the process of finding a maximum matching in non-bipartite graph. In order to accelerate the finding, simple greedy method is used to perform initialization of matching and BFS algorithm is also used in constructing an alternating tree in a non-bipartite graph.The research discussed the finding of maximum  matching in non-bipartite graph using Edmonds’ cardinality matching algorithm. In addition, this research gave a sample of its application in the resolution of The Battle of Britain case. The result obtained is a maximum matching in non-bipartite graph. The maximum matching obtained is a solution to the case of The Battle of Britain.

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Journal Info

Abbrev

Math

Publisher

Subject

Mathematics

Description

Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh ...