VCG auction — polynomial-time algorithm when bidders are unit demand

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Is there a polynomial time algorithm to run a VCG when bidders are unit-demand? I though to look at the Bipartite graph when the left side is the bidders the right is the items and the edges are the values from the bidders to the items. But then I thought of finding the max flow when every time deleting the vertices that took part in it but that wouldn't work. Any ideas?

thanks,