Good morning list, I have decided on a better termination condition for searching for a cyclic superhub. I re-describe below the algorithm:

Start with `i` = 0 and a set of known nodes, including our own node. Iterate over `i`: - Compute hash = H(i || pubkey) for each node. H = RIPEMD160 . SHA256, serialize `i` as a big-endian 32-bit number. Also compute our_hash = H(i || our_pubkey) for our self. Put this in a working set. - Iterate over bits (start with the 7th bit (128) of the first byte): - - Split the working set into two sets, the matching set and the non-matching set, where the bit in the hash matches the bit in our_hash. - - If the non-matching set is empty, skip to the next bit. - - If the matching set is 1 or 2 members, or the non-matching set is 1 or 2 members, merge the two sets together into the working set and exit this loop: we have found a cyclic superhub. - - else set the working set to the matching set. - Sort the set according to the hash (treat the hash as a 160-bit big-endian number). - We should open a channel to the node after us in the sorted list; if we are the last, wrap around to the first node in the list. Regards, ZmnSCPxj Sent with [ProtonMail](https://protonmail.com) Secure Email. ‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐ On March 23, 2018 11:29 PM, ZmnSCPxj <zmnsc...@protonmail.com> wrote: > Good morning list, > > Igor Cota has started implementing my idea: > https://github.com/icota/presto/commit/3311785e660d840f0ac8f2e333d0f0097aec980e > > This forced me to actually start thinking more deeply about the algorithm I > gave. > > 1. We should use a well-used hash algorithm, such as RIPEMD160(SHA256(x)) > 2. We should specify the size of `i` - 32-bits, 4 bytes - and indicate its > endianness. Let us use big-endian, as is typical for the rest of Lightning > and for network order. > 3. My original algorithm had a significant probability of diverging. So I > respecify the termination condition later. > 4. Our own node should be part of the original working set. > 5. In the decimation loop, start with the highest bit. This is the 7-index > bit (1 << 7) of the first byte in the 20-byte hash (we treat the hash as a > big-endian 160-bit number). > > The modified termination condition for the decimation loop is below: > > * If the working set is 7 nodes or more, decimate (i.e. match the next bit in > the hashes and remove those that do not match our own hash in that bit.). > * If the working set is 3 to 6 nodes, stop, that is now the members of the > superhub and we then sort them by hash and decide our position in the > superhub (who will channel to us and who we will channel to). > * If the working set is 1 or 2 nodes, fail to form a superhub. Increment `i` > and restart. > > Regards, > ZmnSCPxj > > Sent with [ProtonMail](https://protonmail.com) Secure Email. > > ‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐ > On March 20, 2018 11:19 AM, ZmnSCPxj via Lightning-dev > <lightning-dev@lists.linuxfoundation.org> wrote: > >> 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. >> >> -- >> >> 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. >> >> --- >> >> 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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