The paper just describes a new method for selecting the main chain. Bitcoin uses the longest chain (with the most work) whereas this paper wants to use the block that is the child of the heaviest sub tree.

The ledger would still be a chain of blocks.

For real tree like blockchains there are a few examples such as IOTA, raiblocks and byteball.

What would trees give you for the usual ledger use case? Or would it be some other use?

Thank you so much for this. I work in this field and have been telling my coworkers that a tree or graph would make more sense. This is what i needed. Thank you

Do you know if anyone is working to implement something like this?

https://archain.org and their "Blockweave" construction sounds similar. Here is a recent talk from Code Mesh on what they're building: https://m.youtube.com/watch?v=YO3zyQvL3Yg

hashgraph?

https://hashgraph.com/

Spectre is super interesting, same author, they started https://www.daglabs.com to implement this

https://medium.com/@avivzohar/the-spectre-protocol-7dbbebb70...

https://eprint.iacr.org/2016/1159.pdf

Ethereum has something along these lines in production; it's how they get higher throughput and 15-second block times.

Please tell me this is how the internet will work in space.

Ethereum actually uses a reduced version of this to accept portions of competing chains so as to be more efficient.