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想明白了

Posted by Ruby931031 at 2013-05-21 14:29:41 on Problem 3686
In Reply To:KM算法在左右两边点数不相等的时候到底应该怎么办?个人觉得网上大多数解题报告有问题 Posted by:Ruby931031 at 2013-05-20 14:29:23
左右两边点数不等时,KM算法的正确性也是可以得到保证的。原因如下:
由KM算法中可行点标的定义,有:
任意匹配的权值 <= 该匹配所覆盖的所有点的顶标值 <= KM算法所得到的匹配所覆盖的所有点的顶标值 = KM算法所得到的的匹配的权值

上面的证明与网上大多数证明不同点在于,网上的证明中只是模糊地说“图中所有点的顶标值”,这只在两点集点数相等时才正确。

上面第二个不等号最为关键,它的理由是:假定|X|<=|Y|,则任意时刻,Y集合中KM算法所取的匹配未覆盖的点的顶标必为0!

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