By Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, Laurence A. Wolsey

In 1958, Ralph E. Gomory reworked the sector of integer programming whilst he released a paper that defined a cutting-plane set of rules for natural integer courses and introduced that the tactic will be subtle to offer a finite set of rules for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a unique workshop celebrating fifty years of integer programming was once held in Aussois, France, as a part of the twelfth Combinatorial Optimization Workshop. It comprises reprints of key ancient articles and written types of survey lectures on six of the most well liked subject matters within the box by means of wonderful participants of the integer programming group. worthy for somebody in arithmetic, machine technology and operations examine, this publication exposes mathematical optimization, particularly integer programming and combinatorial optimization, to a wide viewers.

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Paths, Flows, Matchings, Springer, Berlin, 2003. 2 The Hungarian Method for the Assignment Problem 31 32 Harold W. W. Kuhn, The Hungarian Method for the Assignment Problem, Naval Research Logistics Quarterly 2 (1955) 83–97. 2 The Hungarian Method for the Assignment Problem 33 34 Harold W. Kuhn 2 The Hungarian Method for the Assignment Problem 35 36 Harold W. Kuhn 2 The Hungarian Method for the Assignment Problem 37 38 Harold W. Kuhn 2 The Hungarian Method for the Assignment Problem 39 40 Harold W.

I then realized that Egerv´ary’s paper gave a computationally trivial method for reducing the general assignment problem to a 0-1 problem. Thus, by putting the two ideas together, the Hungarian Method was born. I tested the algorithm by solving 12 by 12 problems with random 3-digit ratings by hand. I could do any such problem, with pencil and paper, in no more than 2 hours. This seemed to be much better than any other method known at the time. The paper was published in Naval Research Logistics Quarterly.

Johnson 1 Solution of a Large-Scale Traveling-Salesman Problem 23 24 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson 1 Solution of a Large-Scale Traveling-Salesman Problem 25 26 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson 1 Solution of a Large-Scale Traveling-Salesman Problem 27 28 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson Chapter 2 The Hungarian Method for the Assignment Problem Harold W. Kuhn Introduction by Harold W. Kuhn 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.