An algorithmic approach to dual integrality of matching and extensions

Abstract

Cunningham and Marsh (1978) announced an algorithm to obtain an integral optimum dual solution of weighted matching when every edge weight is integral. Obtaining such a solution is of interest because it reveals min–max properties. This paper provides a faster algorithm to achieve the same purpose. Our method can be extended to b-matching. Although the existence of an integral optimum dual solution of weighted b-matching was shown by Pulleyblank (1980), this is the first algorithmic way to find such a solution.