How to linearize your cluster

[stefanwouldgo]

@ajtowns

If you have txs A at f/s = 100/1f/s=100/1f/s = 100/1, B at 3980/50, C at 920/49 (with \lambda=5000/100=50λ=5000/100=50\lambda=5000/100=50), and where C spends B and B spends A, what’s the flow diagram that tells you the first/best breakpoint is AB vs C, rather than A vs BC?

In this case the weights are 100-50=50 for A, 3980-2500=1480 for B, and 920-2450=-1530 for C. So the min-cut will pick AB as first subset/chunk.

Next you can choose to see if optimizing AB further is even better: the new \lambda is the new breakpoint is the combined feerate of AB, which is 4080/51=80. Then the new weights become 20 for A, -20 for B, -3000 for C. So the min-cut will pick A as the next best chunk. We could let the algorithm run again with the new breakpoint \lambda=100 and see that now we get the empty set or maybe A again, but we already know that a single node cannot be improved upon, so the optimal chunking is (A,B,C).