Good morning Benjamin,
Rusty simulated an older version of my idea here; C code near the end of the
message: https://lists.ozlabs.org/pipermail/c-lightning/2018-April/000029.html
However this has a bug: I specify that:
>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.
The code there does not implement the check "if the candidate has a channel
with us", leading to smaller reachability since nodes who could afford to
create multiple channels will create multiple channels to the same peer in the
simulation.
A naive analysis suggests that if only one node in the entire network uses the
algorithm I described, it should be indistinguishable from a random connection
policy, so a naive analysis suggests that something has gone wrong if the
reachability of this algorithm is significantly less than the reachability of a
random connection algorithm. The simulation also does not consider that
existing nodes may break old channels or make new channels themselves; it is
not certain how often that happens on the real network.
Regards,
ZmnSCPxj
Sent with [ProtonMail](https://protonmail.com) Secure Email.
‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐
On April 19, 2018 7:56 AM, Benjamin Mord <ben@mord.family> wrote:
> Elegant idea.
>
> Is there a simulation platform yet for experimenting with ideas such as this?
> I imagine it may sometimes be useful to empirically test aggregate effects of
> different routing heuristics, however naive or artificial the underlying
> assumptions may need to be.
>
> Is there an API, perhaps implementation agnostic, to separate such strategies
> from the protocol itself?
>
> Is there a place yet to specify such heuristics where tight coordination on
> details are of mutual benefit, such as a bolt?
>
> On Sat, Mar 24, 2018, 8:08 AM ZmnSCPxj via Lightning-dev
> <lightning-dev@lists.linuxfoundation.org> wrote:
>
>> 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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