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This is one of the biggest problems with Blockchains right now. If it cannot be solved then their utility is extremely limited. There are two main approaches that seem likely to work:

- "Layer 2" networks: Most transaction volume happens off-chain. POW blockchain remains as a settlement layer. Quite a few proposed protocols. Lightning network [1] is the most well known. First mainnet lightning transactions were sent in December [2]

- Sharding: Split the blockchain into lots of different blockchains with a subset of miners validating transactions on each sub-chain. Miners are randomly assigned a new sub-chain on a regular basis to stop collusion. Each sub-chain has it's own address space. Sub-chains can communicate using asynchronus message passing. Ethereum has a draft specification [3][4] and is starting to implement some test clients [5].

[1] https://lightning.network/

[2] https://twitter.com/alexbosworth/status/946175898029395968

[3] https://github.com/ethereum/sharding/blob/develop/docs/doc.m...

[4] https://github.com/ethereum/wiki/wiki/Sharding-FAQ

[5] https://blog.ethereum.org/2018/01/02/ethereum-scalability-re...

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