Decentralized cryptocurrency systems, known as blockchains, have shown
promise as an infrastructure for mutually distrustful parties to
securely agree on transactions. Nevertheless, blockchain systems are
constrained by the CAP Trilemma. Due to performance degradation, it is
impossible to address this issue by improving simply the consensus layer
or the network layer. To alleviate the CAP constraint in consortium
blockchains, we propose a topological construction method to optimize
the physical layer based on multi-dimensional hypercubes with excellent
partition tolerance in probability. The basic topology has the advantage
of solving the mismatch problem between the overlay network and the
underlying network. It is further extended to hierarchical recursive
topologies with more intermediate links or short links to balance the
reliability requirement with the cost of building the physical network.
We prove that the proposed hypercube topology has better partition
tolerance than the regular rooted tree and ring lattice topologies, and
effectively fits the upper-layer protocols at the consensus and network
layers. As a result, combined with suitable transmission and consensus
protocols that satisfy strong consistency and availability, the proposed
topology-constructed blockchain can reach the CAP guarantee bound.