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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.
This algorithm may yield a non-optimal solution. For example, suppose there are two tasks and two agents with costs as follows: Alice: Task 1 = 1, Task 2 = 2. George: Task 1 = 5, Task 2 = 8. The greedy algorithm would assign Task 1 to Alice and Task 2 to George, for a total cost of 9; but the reverse assignment has a total cost of 7.
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%
The Hungarian algorithm solves the assignment problem and it was one of the beginnings of combinatorial optimization algorithms. It uses a modified shortest path search in the augmenting path algorithm.
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
The algorithm constructs a schedule in iterations, where during iteration a tentative selection of items to bin is selected. The selection for bin b j {\displaystyle b_{j}} might change as items might be reselected in a later iteration for other bins.
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The implementation of a classifier that knows that its input set consists of one example from each class might first compute a goodness-of-fit score for each of the c 2 possible pairings of an example to a class, and then employ the Hungarian algorithm to maximize the sum of the c selected scores over all c! possible ways to assign exactly one ...