Minimum weight cut by product instead of sum in a undirected graph

Question

All algorithms I could find use the maximum flow/minimum cut property to calculate a minimum weighted cut that separates the source from the sink. However, all these algorithms use the sum of the weights as their definition of the minimum, while in my use case the weights are not absolute numbers, but chances, and thus have to be minimal under multiplication instead of addition to provide the proper minimum cut.

I was not able to prove that the ideas and properties behind the known max flow/min cut algorithms still hold under multiplication instead of addition. Can these algorithms be adjusted for a minimum product weight cut? If not, what algorithms could I use to calculate such a cut?

Answer 1

Can these algorithms be adjusted for a minimum product weight cut?

Yes, use log probabilities as capacities.