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 remodeled the sphere 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 should be subtle to offer a finite set of rules for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a different workshop celebrating fifty years of integer programming was once held in Aussois, France, as a part of the twelfth Combinatorial Optimization Workshop. It includes reprints of key ancient articles and written models of survey lectures on six of the most popular issues within the box by means of exotic contributors of the integer programming neighborhood. worthwhile for an individual in arithmetic, desktop technological know-how and operations study, this booklet exposes mathematical optimization, in particular integer programming and combinatorial optimization, to a huge viewers.

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**Sample text**

The SEAC had a liquid mercury memory system which was extremely limiting. During that summer, I was reading K¨onig’s book on graph theory. I recognized the following theorem of K¨onig to be a pre-linear programming example of duality: If the numbers of a matrix are 0’s and 1’s, then the minimum number of rows and columns that will contain all of the 1’s is equal to the maximum number of 1’s that can be chosen, with no two in the same row or column. Harold W. edu M. Jünger et al. 1007/978-3-540-68279-0_2, © Springer-Verlag Berlin Heidelberg 2010 29 30 Harold W.

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.

The SEAC (Standard Eastern Automatic Computer), housed in the National Bureau of Standards in Washington, could solve linear programs with about 25 variables and 25 constraints. The SEAC had a liquid mercury memory system which was extremely limiting. During that summer, I was reading K¨onig’s book on graph theory. I recognized the following theorem of K¨onig to be a pre-linear programming example of duality: If the numbers of a matrix are 0’s and 1’s, then the minimum number of rows and columns that will contain all of the 1’s is equal to the maximum number of 1’s that can be chosen, with no two in the same row or column.