[Lightning-dev] Towards a gridlike Lightning Network

[ZmnSCPxj]

Good morning list,

As my award-winning and supremely notable and talked-about-by-the-man-on-the-street article "Cyclic Superhubs as Solution Towards Reasonable Lightning Network Topography" points out, cycles are a good way to organize the LN in order to allow easier accessibility to the network for all participants of all kinds.

An issue here is the need for coordination in order to set up cyclic superhubs.  A node acting by itself cannot form cyclic superhubs.

However, one can consider that coordination is needed only to identify peers with which one forms superhubs.  But we already have a system that identifies peers: the node gossip.

So let us assume: All nodes have similar-enough views of the publicly-visible peers on the node graph, as built by node gossip.

I now present an algorithm, which given a set of nodes extracted from node gossip, returns a peer to try connecting and funding a channel to.

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First, start with a 32-bit number i = 0.

For each node, get hash = H(i || pubkey), where H is some standard hash algorithm, and pubkey is the public key of the node.  Also get our_hash = H(i || our_pubkey)

Perform successive filtering.  While the set is larger than 2 nodes, successively compare high bits.  If the highest bit of hash does not match the highest bit of our_hash, remove it from the set.  If the resulting set is still larger than 2, match the next bit.  When the set is now 2 or 1 node, back off by one bit and add back the most recently removed nodes.  This yields a set that is at least 3 or more nodes.

Sort the nodes according to hash.

Identify where our node is in the sorted list.  Then our candidate is the next node in the list, or if we are the last node, then the first node in the list.

If the candidate already has a channel with us, or has no address info and cannot be found by DNS seed or so on, or cannot be contacted, or refuses incoming channels or some other error, then increment i and try finding again.

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Even if nodes have some divergence in their own local maps of the network, there is the chance that the difference will be filtered away and the nodes that are "destined" to form a superhub can still find each other in the same superhub.

Assuming all nodes have the same routemap, then all nodes will form their own, non-overlapping superhubs for each i.  However if some nodes get to increment i, hopefully because it already has a channel with its destined candidate peer at one value of i, it can then potentially form superhubs with other nodes that have also reached higher i.

Regards,
ZmnSCPxj
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