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What is a min_fee?

Having a min_fee means changing the fee calculation to max(min_fee, fee_rate * amt), potentially replacing the base_fee. My reasoning behind this is that it prevents 0-fee payments – fees below 1 msat are currently rounded down to 0 – without setting a min_htlc_msat or base_fee.

How does it help?

Not setting a min_htlc_msat makes sure that micropayments can still be routed, while not setting a base_fee ensures a linear fee function for Pickhardt payments.
While my proposed fee function is generally not linear, it can be ensured that it always is linear in practice. I showed this in a reddit thread, responding to Rene Pickhardt. Here's my response in full, if you don't want to go to that reddit thread:

My idea behind max(min_fee, fee_rate * amt) was the fact that for reasonable min_fee and fee_rate settings, the function is linear even for relatively small payments.

More exactly, the function is linear for fee_rate * amt >= min_fee – or equivalently amt >= min_fee / fee_rate (let's call this the fee_ratio).

A wallet/node that uses your flooding algorithm – with, say, a minimum split size of 10k sats – could then heuristically ignore channels that:

  1. Have any base fee
  2. Have a fee_ratio that is greater than 10k sats, which should be incredibly rare

Most channels would probably have their min_fee set to 1 msat, simply to prevent 0-fee htlcs. In my 200 ppm example, the fee_ratio would be 5 sats.

In fact, just 1k sats is a magic number here! When the min_fee is 1 msat, then any channel with a nonzero fee_rate has a maximum fee_ratio of 1k sats (0.001 / 0.000001 = 1000)!

So even all the way down to 1k sat payment splits, any channel with a 1 msat min_fee – and a nonzero fee_rate – has a linear fee function.

Is it a good idea?

Now I would like to know if there are any fundamental issues here that I'm missing.
It seems to me that it could serve as a replacement for the (iirc arbitrary) base_fee setting, while still allowing Pickhardt payments.

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Note: Probably this should be a comment, but I don't have enough reputation, so I'll let it grow as an answer.

There is something I don't understand about this: why do you state that the fee function you propose is linear?

Let's say I set 10 msat/sat feerate and 100 msat min_fee. Payments from 1 msat all the way up to 10 sats would all pay a 100 msat fee. Only larger payments would start to pay more. This is not linear: it's constant up to some arbitrary amount and then it becomes linear increasing.

The base_fee + feerate model instead is really linear, starting off at base_fee for 0-amt payments and growing linearly from there.

So: your system is linear only in the special case where you set a really small min_fee, while the currently implemented system is always linear. If you want to solve the fact that small payments pay a too large fee, you can just set a lower base_fee (down to 1msat) and possibly a higher feerate. With such a settings the two systems are practically equivalent.

Now, I'm not familiar with Pickardt payments, so ther might be something there that would change everything.

TLDR: your system is practically linear only in case of very low min_fee and in this case it very much looks like the current system with low base_fee.

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    f(x) = ax +b is the current fee model. For a function to be linear it is not sufficient that the plot looks like a straight line but rather the following equation needs to hold f(x+y) =f(x) + f(y) now it is easy to see that f(x+y) + b = f(x) + f(y) which only implies linearity if and only if b=0. That being said the proposed function with the max is also not linear and also at f(0) not even convex Aug 26 at 10:39
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    Oh, you need the precise notion of linearity. But then you need to have that f(0)=0 and as far as I understood we don't want to have free 0-amt payments. Looks like there's no clear way out then...
    – St3p
    Aug 26 at 13:42
  • of course f(0)=0 is necessary as we don't want to pay channels if we don't send something over them. but maybe I miss your point here. anyway your answer lead me to also write a much longer post on the mailinglist so I drop that here for reference: lists.linuxfoundation.org/pipermail/lightning-dev/2021-August/… Aug 26 at 14:57

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