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.

中文翻译：

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匹配和扩展的双重完整性的算法方法

Cunningham和Marsh（1978）宣布了一种算法，该算法在每个边缘权重都为整数时获得加权匹配的整体最优对偶解。获得这样的解决方案很有趣，因为它揭示了最小到最大的特性。本文提供了一种更快的算法来达到相同的目的。我们的方法可以扩展到$b$-匹配。虽然存在加权的整体最优对偶解$b$Pulleyblank（1980）展示了-matching，这是找到这种解决方案的第一种算法。