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I've heard that there is such a dilemma for LN: if channel states were not published, the payer will not able to find any viable path, unless he takes brute-force-like probing approach (which looks quite unscalable); if the channel states were meant to published, the economic privacy of LN users would be sacrificed.

Does such dilemma exist? If such idea is wrong, why?

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I suggest we say channel balance instead of channel state (the state is encoded by a signed commitment TX and if it leaks you could loose your funds)

As for the balance such a dilemma indeed exists. Indeed routing becomes more trial and error without public channel balances. Yet, there will probably be methods that allow to predict routes with higher probability.

On the other hand, there is not only the privacy aspect speaking against public channel balances. One would have to announce every balance update to the network which happens for every payment and would result in an infeasible high payload of gossip messages.

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To add to Rene’s answer: The protocol design currently allows the probing of viable paths to leak just enough information to let you determine whether all channels along route provide adequate liquidity or not, without revealing the individual channel balances.

Note though that one could use probing (receiver and sender controlled by same individual) with different routes and amounts to derive/compute the exact or approximate liquidity in a given channel of interest.

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    However, this is only reveals the liquidity that a channel node is willing to offer for routing. There is nothing in the protocol that enforces a node to offer all its liquidity for routing. – James C. Jan 11 at 15:07

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