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The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods.It was developed and published in 1955 by Harold Kuhn, who gave it the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry.
In the balanced assignment problem, both parts of the bipartite graph have the same number of vertices, denoted by n. One of the first polynomial-time algorithms for balanced assignment was the Hungarian algorithm. It is a global algorithm – it is based on improving a matching along augmenting paths (alternating paths between unmatched vertices
Hungarian algorithm unbalanced assignment problem example: Image title: Worked example of minimising costs by assigning tasks to an unequal number of workers using the Hungarian method, by CMG Lee. Width: 100%: Height: 100%
Harold William Kuhn (July 29, 1925 – July 2, 2014) was an American mathematician who studied game theory.He won the 1980 John von Neumann Theory Prize jointly with David Gale and Albert W. Tucker.
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This contribution was translated and published in 1955 by Harold W. Kuhn, [6] who also showed how to apply Kőnig's and Egerváry's method to solve the assignment problem; the resulting algorithm has since been known as the "Hungarian method". [7]
The formal definition of the bottleneck assignment problem is Given two sets, A and T, together with a weight function C : A × T → R. Find a bijection f : A → T such that the cost function: (, ()) is minimized.