Efficient dual simplex algorithms for the assignment problem

Donald Goldfarb

Abstract: Efficient algorithms based upon Balinski's signature method are described for solving then × n assignment problem. These algorithms are special variants of the dual simplex method and are shown to have computational bounds of O(n 3). Variants for solving sparse assignment problems withm arcs that require O(m) space and O(mn + n 2 logn) time in the worst case are also presented.