Topic

# Hungarian algorithm

About: Hungarian algorithm is a research topic. Over the lifetime, 861 publications have been published within this topic receiving 25097 citations. The topic is also known as: Kuhn–Munkres algorithm & Munkres assignment algorithm.

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TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.

Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.

11,096 citations

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TL;DR: In this paper, algorithms for the solution of the general assignment and transportation problems are presen, and the algorithm is generalized to one for the transportation problem.

Abstract: In this paper we presen algorithms for the solution of the general assignment and transportation problems. In Section 1, a statement of the algorithm for the assignment problem appears, along with a proof for the correctness of the algorithm. The remarks which constitute the proof are incorporated parenthetically into the statement of the algorithm. Following this appears a discussion of certain theoretical aspects of the problem. In Section 2, the algorithm is generalized to one for the transportation problem. The algorithm of that section is stated as concisely as possible, with theoretical remarks omitted.

3,918 citations

01 Jan 2010

TL;DR: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory.

Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.

3,108 citations

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CERN

^{1}TL;DR: The assignment problem, together with Munkres proposed algorithm for its solution in square matrices, is presented and an extension of this algorithm which permits a solution for rectangular matrices is developed.

Abstract: The assignment problem, together with Munkres proposed algorithm for its solution in square matrices, is presented first. Then the authors develop an extension of this algorithm which permits a solution for rectangular matrices.Timing results obtained by using an adapted version of Silver's Algol procedure are discussed, and a relation between solution time and problem size is given.

530 citations

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TL;DR: In this paper, the Hungarian method is used to find the minimal cost assignment and the best assignment after excluding the minimum cost assignment, which can be used to rank all the assignments in a sequence in order of cost.

Abstract: The Hungarian method gives an efficient algorithm for finding the minimal cost assignment. However, in some cases it may be useful to determine the second minimal assignment (i.e., the best assignment after excluding the minimal cost assignment) and in general the kth minimal assignment for k = 1, 2, …. These things can easily be determined if all the assignments can be arranged as a sequence in increasing order of cost. This paper describes an efficient algorithm for such a ranking of all the assignments. The maximum computational effort required to generate an additional assignment in the sequence is that of solving at most (n − 1) different assignment problems, one each of sizes 2, 3, …, n.

478 citations