This proposal consist into solving a Min Cost flow network problem in the context of a state-channel based payment protocol, where payments between partecipants flow based on the shortes and cheapest path between the two nodes. This specific problem is a mixture of the shortest path problem with the classical NF problem , whereby the cost of taking a specific path is the sum of the fixed fees along the path plus the sum of the variable fee rates (that are proportional to the amount of the payment flowing across the edge).

The dataset to tackle the problem has already been retrieved with some tools of the LND suite. Minor fixes and addons can be executed with the mempool.space APIs, targeting specific nodes and channels.