PENENTUAN MATCHING MAKSIMUM PADA GRAF BIPARTIT BERBOBOT MENGGUNAKAN METODE HUNGARIAN

Muchammad Abrori, Rina Wahyuningsih

DOI: https://doi.org/10.23917/jiti.v11i1.984

Abstract

Matching is a part of graph theory that discuss to make a pair, that can be used to solve many problems; one of them is the assignment problem. The assignment problem is to make a pair problem for n as the employees and for n as the duties, therefore each employee gets one duty, and each duty is given exactly for each employee. The assignment problem can be solved by determining the matching in weighted bipartite graph through Hungarian Method. It can be determined from the alternating tree of a formed edge. If there is augmenting path, that augmenting path is used to form the more number of matching. If the formed path is alternating path, therefore the process is labeling the new node until finding the augmenting vertices. This matching is called as the perfect matching with the number of maximum weighed side in weighted bipartite graphs. The result matching is the solution for the assignment problem by giving an employee with a duty.

Keywords

matching; graph; assignment problem; Hungarian method

References

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