Fast Transaction Scheduling in Blockchain Sharding

Sharding is a promising technique for addressing the scalability issues of blockchain, and this technique is especially important for IoT, edge, or mobile computing. It divides the $n$ participating nodes into $s$ disjoint groups called shards, where each shard processes transactions in parallel. We examine batch scheduling problems on the shard graph $G_s$, where we find efficient schedules for a set of transactions. First, we present a centralized scheduler where one of the shards is considered as a leader, who receives the transaction information from all of the other shards and determines the schedule to process the transactions. For general graphs, where a transaction and its accessing objects are arbitrarily far from each other with a maximum distance $d$, the centralized scheduler provides $O(kd)$ approximation to the optimal schedule, where $k$ is the maximum number of shards each transaction accesses. Next, we provide a centralized scheduler with a bucketing approach that offers improved bounds for the case where $G_s$ is a line graph, or the $k$ objects are randomly selected. Finally, we provide a distributed scheduler where shards do not require global transaction information. We achieve this by using a hierarchical clustering of the shards and using the centralized scheduler in each cluster. We show that the distributed scheduler has a competitive ratio of $O(A_{CS} \cdot \log d \cdot \log s)$, where $A_{CS}$ is the approximation ratio of the centralized scheduler. To our knowledge, we are the first to give provably fast transaction scheduling algorithms for blockchain sharding systems. We also present simulation results for our schedulers and compare their performance with a lock-based approach. The results show that our schedulers are generally better with up to 3x lower latency and 2x higher throughput.