I would like to propose a new BIP to bitcoin called BlockReduce.  BlockReduce presents a new blockchain topology that offers 3+ orders of magnitude improvement in transaction throughput while avoiding the introduction of hierarchical power structures and centralization. This is accomplished through a modification to the block reward incentive to not only reward work, but to also reward optimization of network constraints and efficient propagation of transactions. This is accomplished by creating a Proof-of-Work (PoW) managed hierarchy of tightly-coupled, merge-mined blockchains.  

BlockReduce is actually highly compatible with the Bitcoin codebase in that in only requires a sharding of state and the introduction of a 268 byte header that allows for 3 levels of merge-mining.  Please checkout a paper outlining BlockReduce here: 

Please let me know if you have any comments or questions.  Also, if you could tell me the process for getting a BIP listed on Github I would appreciate it.

Thanks,