I've read that IOTA would only be truly infinitely scaleable with subtangles because a full node can only process ~1000 transactions per second.
What are subtangles? When will they emerge? What potential problems would arise with them?
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There are various kind of sub-tangles (or clusters). Here are two examples:
Today, with the Coordinator
According my understanding, a subtangle is build by a subset of fullnodes disconnected from the main tangle. (The main tangle being the one were the Coo broadcast the milestones.)
A subtangle cannot receive milestones and therefore, validation of transactions is driven only by probability. Participants in a subtangle must trust probability instead of coordinator !
If one day, the subtangle is re-connected with the main tangle: all it's transactions will be seen as "not confirmed yet" because no milestone transaction is validating them. To get those transactions confirmed, the fullnodes previously in the subtangle must rebroadcast all those transactions to the main tangle so that they get validated by the coordinator. In case of double spend, the coordinator won't validate them: end of the story. If rebroadcasted transaction is approved by coordinator: fine, end of the story.
Tomorrow, without Coordinator
(disclaimer: please note that this just my understanding of the protocol, don't take it for true. Don't hesitate to comment to invalidate -or approve- this vision)
There is no way to make the distinction between the main tangle and the subtangle because there is no more milestone transaction. In fact we don't have a main tangle and a subtangle: we only have two tangles (probably a huge one and a small one).
If, one day the 2 tangles are merged all transactions that were trusted on the small tangle because validated by let's say 99,99 % of the transactions of the small tangle will suddenly see this validation ratio drop down to let's say 0,1% (this percentage depends on the relative size of the 2 tangles). So we are in a situation were transactions that were trusted on small tangle aren't trusted anymore. Solution is to rebroadcat all transactions from one tangle to the other so that they get approved by a majority... Transactions from the small tangle that are conflicting with transactions on the big tangle will remain unconfirmed. This is a threat for all participants that previously trusted the small tangle.
If both tangles are approximately of the same size: all trusted transactions will see their validation ratio suddenly drop to about 50%. It may take some time to reach a validation ratio acceptable for the majority of those transactions, but at some point: the tangle will be healthy again. (by healthy I mean that we will see significant validation ratio (99% +) again).