Georgia Institute of Technology College of Sciences

Fifty five years ago, two results of the Hungarian mathematicians, Koenig and Egervary, were combined using the duality theory of linear programming to construct the Hungarian Method for the Assignment Problem. In a recent reexamination of the geometric interpretation of the algorithm (proposed by Schmid in 1978) as a steepest descent method, several variations on the algorithm have been uncovered, which seem to deserve further study. The lecture will be self-contained, assuming little beyond the duality theory of linear programming. The Hungarian Method will be explained at an elementary level and will be illustrated by several examples. We shall conclude with account of a posthumous paper of Jacobi containing an algorithm developed by him prior to 1851 that is essentially identical to the Hungarian Method, thus anticipating the results of Koenig (1931), Egervary (1931), and Kuhn (1955) by many decades.