Maximum Flow with Bipartite Matching

Öz

In this study, the maximum flow problem in all networks that can be modeled on bipartite networks has been solved. The maximum flow problem refers to the maximum flow capacity reached between source and sink nodes on a network. There are different types of approaches to solving the maximum flow problem. One of these popular methods is matching methods. In this study, it is aimed to calculate maximum flow values for bipartite graph types. For the solution, Malatya Matchin algorithm (MMA), which gives optimum matching results in bipartite graphs, was used. MMA gives optimum results in unweighted bipartite graph types. In this study, the application was carried out on unweighted random bipartite graphs produced with the Erdos reyni model and optimum results were achieved. R programming language and igraph library were used to implement the algorithm and design the networks.

Anahtar Kelimeler

• Maximum Bipartite Matching
• Maximum Flow
• Malatya Matching Algorithm

İki Parçalı Eşleştirme ile Maksimum Akış

Öz

Bu çalışmada bipartite ağlar üzerinde modellenebilen tüm ağlardaki maksimum akış probleminin çözümü gerçekleştirilmiştir. Maksimum flow problemi bir ağ üzerindeki source ve sink düğümleri arasında ulaşılan maksimum akış kapasitesini ifade etmektedir. Maksimum flow probleminin çözümü için farklı yaklaşım türleri mevcuttur. Bu popüler yöntemlerden bir tanesi eşleştirme(matching) yöntemleridir. Bu çalışmada bipartite çizge türlerine yönelik maksimum akış değerleri hesaplanması hedeflenmiştir. Çözüm için bipartite çizgelerde optimum matching sonuçlarını veren Malatya Matching algoritması(MMA) kullanılmıştır. MMA ağırlıksız bipartite çizge türlerinde optimum sonucu vermektedir. Bu çalışmada Erdos reyni model ile üretilen ağırlıksız rastgele bipartite çizgelerde uygulama gerçekleştirilmiş ve optimum sonuçlara ulaşılmıştır. Algoritmanın uygulanması ve ağların tasarlanmasında R programlama dili ve igraph kütüphanesi kullanılmıştır.

Anahtar Kelimeler

• Maksimum Bipartite Eşleştirme
• Maksimum Akış
• Malatya Matching Algoritması

Kaynakça

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