Chapter overview:
  * How path finding works in the network

Relevant questions to answer:
  * What is packet switching? What is circuit switching? Which one does LN use today?
  * In the abstract what is path finding?
  * What is dijkstra's? What modifications need to be made to apply it to this domain?
  * Why must path finding happen backwards (receiver to sender)?
  * How is the information contained in a channel update used in path finding?
  * How can errors sent during payment routing help the sender to narrow their search space?
  * What is payment splitting? How does it work?
  * What information can be sent to intermediate and the final node aside from the critical routing data?
  * What are multi-hop locks? What addition privacy and security guarantees to they offer?
  * How can the flexible onion space be used to enabled packet switching in the network?




==== Finding a path

Payments on the Lightning Network are forwarded along a path of channels from one participant to another.
Thus, a path of payment channels has to be selected.
If we knew the exact channel balances of every channel we could easily compute a payment path using any of the standard path finding algorithms taught in any computer science program.
This could even be done in a way to optimize the fees that would have to be paid by the payer to the nodes that kindly forward the payment.
However, as discussed the balance information of all channels is and cannot be available to all participants of the network.
Thus, we need to have one or more innovative path finding strategy.
These strategies must relate closely to the routing algorithm that is used.
As we will see in the next section, the Lightning Network uses a source based onion routing protocol for routing payments.
This means in particular that the sender of the payment has to find a path through the network.
With only partial information about the network topology available this is a real challenge and active research is still being conducted into optimizing this part of the Lightning Network implementations.
The fact that the path finding problem is not fully solved for the case of the Lightning Network is a major point of criticism towards the technology.
The path finding strategy currently implemented in Lightning nodes is to probe paths until one is found that has enough liquidity to forward the payment.
While this is not optimal and certainly can be improved, it should be noted that even this simplistic strategy works well.
This probing is done by the Lightning node or wallet and is not directly seen by the user of the software.
The user might only realize that probing is taking place if the payment is not going through instantly.
The algorithm currently also does not necessarily result in the path with the lowest fees.
=======
=== What is "Source-Based" routing and why does the Lightning Network use it?

Source-based routing is a method of path-finding where the sender (i.e. the source) plans the route from itself, through the intermediary nodes, and finally to the destination.
Once a path has been selected, the sender sends the payment to the first intermediary node, who sends it to the second intermediary node and so on, until it reaches the destination.
While a payment is in-flight along a path, the path typically does not get changed by any of the intermediary nodes, even if a shorter path or a cheaper path (in terms of routing fees) exists.


The Lightning Network uses source-based routing at the time of writing in order to protect user privacy.
As discussed in the chapter on Onion Routing, the intermediary nodes transmitting the payment are not aware of the full path of the payment; they only know the node they received it from and the node they are sending it to.

We also cannot expect the destination to find a path.
Even if it specifies a path in the invoice, that path may no longer be viable by the time the invoice is paid, which could be several minutes or several days later.
The recipient can, however, specify "routing hints" in the invoice that may assist the sender in finding a possible path.

Furthermore, source-based routing comes with some inherent drawbacks.
The sender chooses the path based on their current understanding of the topological map of the Lightning network.
As discussed in previous chapters, this map is necessarily incomplete; the sender may not be aware of all the channels, and even if they are they will almost certainly not know the latest balances in each of the channels.
And even if the sender did have a complete topological map at one point in time, the balances of channels change with every payment, and so in a short space of time the map would become obsolete.
The standard path finding mechanism with source based onion routing that is implemented in all Lightning Network implementations is the following:

1. Select an arbitrary path of payment channels which connects sender and receiver of the payment and for which all channels have a capacity of at least the payment amount and accept HTLCs of this amount.
2. Construct the onion according to the meta data (basefee, feerate, CLTV delta) of the channels.
3. Send out the onion and see if the payment settles by nodes sending back preimages or if the payment fails.
4. If the payment fails use this knowledge to select a different path by starting at step 1.

This means that with every attampted payment nodes actually probe the network and will also learn some information about how balances are distributed.
Implementations will usually prioritice cheaper paths or exclude channels which recently have failed.
In that sense the selection is not completely arbitrary.
Still even with such heuristics in place it could still be considered as a random process or random walk through the channel graph. 
There can be several reasons why the payment may fail along the way.
For example one of the nodes becomes unreachable, doesn't have the channel balance, can't accept new htlcs, has updated its fees to a higher amount, or the channel is closed in the interim.
Furthermore, there is no guarantee that the route chosen was the cheapest in terms of fees, or if a shorter path existed.
As at the time of writing, this is a design trade-off made to protect user privacy.
