This seems absolutely perfect for the Lightning Network! This basically allows you to find the largest and most efficient multipath payment correct?

Here's the scientific paper: https://arxiv-export1.library.cornell.edu/pdf/2203.00671v2

Framed in the context of the Lightning Network:

Given a source (payer) and destination (payee), Max flow is the largest multipath payment that can be made between a source and destination. Min cost is the smallest set of edges (by total capacity) whose removal from the network disconnects the source and destination. What's interesting about min cost and max flow is that they are the same problem.