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.
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.