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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%
Travelling salesman problem; Bottleneck traveling salesman problem; Christofides' heuristic for the TSP; Route inspection problem; Matching Matching; Hopcroft–Karp algorithm for maximum matching in bipartite graphs; Edmonds's algorithm for maximum matching in non-bipartite graphs; Assignment problem; Hungarian algorithm for the assignment problem
A former Professor Emeritus of Mathematics at Princeton University, he is known for the Karush–Kuhn–Tucker conditions, for Kuhn's theorem, and for developing Kuhn poker. He described the Hungarian method for the assignment problem , but a paper by Carl Gustav Jacobi , published posthumously in 1890 in Latin, was later discovered that had ...
In the special case in which all the agents' budgets and all tasks' costs are equal to 1, this problem reduces to the assignment problem. When the costs and profits of all tasks do not vary between different agents, this problem reduces to the multiple knapsack problem. If there is a single agent, then, this problem reduces to the knapsack problem.
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Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.