  Due to its security, transparency, and flexibility in verifying virtual
assets, blockchain has been identified as one of the key technologies for
Metaverse. Unfortunately, blockchain-based Metaverse faces serious challenges
such as massive resource demands, scalability, and security concerns. To
address these issues, this paper proposes a novel sharding-based blockchain
framework, namely MetaShard, for Metaverse applications. Particularly, we first
develop an effective consensus mechanism, namely Proof-of-Engagement, that can
incentivize MUs' data and computing resource contribution. Moreover, to improve
the scalability of MetaShard, we propose an innovative sharding management
scheme to maximize the network's throughput while protecting the shards from
51% attacks. Since the optimization problem is NP-complete, we develop a hybrid
approach that decomposes the problem (using the binary search method) into
sub-problems that can be solved effectively by the Lagrangian method. As a
result, the proposed approach can obtain solutions in polynomial time, thereby
enabling flexible shard reconfiguration and reducing the risk of corruption
from the adversary. Extensive numerical experiments show that, compared to the
state-of-the-art commercial solvers, our proposed approach can achieve up to
66.6% higher throughput in less than 1/30 running time. Moreover, the proposed
approach can achieve global optimal solutions in most experiments.
