// 8. Choose the best route by the lowest total fee.
// As for the actual search algorithm,
- // we do a payee-to-payer Dijkstra's sorting by each node's distance from the payee
- // plus the minimum per-HTLC fee to get from it to another node (aka "shitty A*").
+ // we do a payee-to-payer pseudo-Dijkstra's sorting by each node's distance from the payee
+ // plus the minimum per-HTLC fee to get from it to another node (aka "shitty pseudo-A*").
+ //
+ // We are not a faithful Dijkstra's implementation because we can change values which impact
+ // earlier nodes while processing later nodes. Specifically, if we reach a channel with a lower
+ // liquidity limit (via htlc_maximum_msat, on-chain capacity or assumed liquidity limits) then
+ // the value we are currently attempting to send over a path, we simply reduce the value being
+ // sent along the path for any hops after that channel. This may imply that later fees (which
+ // we've already tabulated) are lower because a smaller value is passing through the channels
+ // (and the proportional fee is thus lower). There isn't a trivial way to recalculate the
+ // channels which were selected earlier (and which may still be used for other paths without a
+ // lower liquidity limit), so we simply accept that some liquidity-limited paths may be
+ // de-preferenced.
+ //
+ // One potentially problematic case for this algorithm would be if there are many
+ // liquidity-limited paths which are liquidity-limited near the destination (ie early in our
+ // graph walking), we may never find a liquidity-unlimited path which has lower proportional
+ // fee (and only lower absolute fee when considering the ultimate value sent). Because we only
+ // consider paths with at least 5% of the total value being sent, the damage from such a case
+ // should be limited, however this could be further reduced in the future by calculating fees
+ // on the amount we wish to route over a path, not the amount we are routing over a path.
+ //
+ // Alternatively, we could store more detailed path information in the heap (targets, below)
+ // and index the best-path map (dist, below) by node *and* HTLC limits, however that would blow
+ // up the runtime significantly both algorithmically (as we'd traverse nodes multiple times)
+ // and practically (as we would need to store dynamically-allocated path information in heap
+ // objects, increasing malloc traffic and indirect memory access significantly). Further, the
+ // results of such an algorithm would likely be biased towards lower-value paths.
+ //
+ // Further, we could return to a faithful Dijkstra's algorithm by rejecting paths with limits
+ // outside of our current search value, running a path search more times to gather candidate
+ // paths at different values. While this may be acceptable, further path searches may increase
+ // runtime for little gain. Specifically, the current algorithm rather efficiently explores the
+ // graph for candidate paths, calculating the maximum value which can realistically be sent at
+ // the same time, remaining generic across different payment values.
+ //
// TODO: There are a few tweaks we could do, including possibly pre-calculating more stuff
// to use as the A* heuristic beyond just the cost to get one node further than the current
// one.