On the Efficiency of Dynamic Transaction Scheduling in Blockchain Sharding

Sharding is a technique to speed up transaction processing in blockchains, where the $n$ processing nodes in the blockchain are divided into $s$ disjoint groups (shards) that can process transactions in parallel. We study dynamic scheduling problems on a shard graph $G_s$ where transactions arrive online over time and are not known in advance. Each transaction may access at most $k$ shards, and we denote by $d$ the worst distance between a transaction and its accessing (destination) shards (the parameter $d$ is unknown to the shards). To handle different values of $d$, we assume a locality sensitive decomposition of $G_s$ into clusters of shards, where every cluster has a leader shard that schedules transactions for the cluster. We first examine the simpler case of the stateless model, where leaders are not aware of the current state of the transaction accounts, and we prove a $O(d \log^2 s \cdot \min\{k, \sqrt{s}\})$ competitive ratio for latency. We then consider the stateful model, where leader shards gather the current state of accounts, and we prove a $O(\log s\cdot \min\{k, \sqrt{s}\}+\log^2 s)$ competitive ratio for latency. Each leader calculates the schedule in polynomial time for each transaction that it processes. We show that for any $\epsilon > 0$, approximating the optimal schedule within a $(\min\{k, \sqrt{s}\})^{1 -\epsilon}$ factor is NP-hard. Hence, our bound for the stateful model is within a poly-log factor from the best possibly achievable. To the best of our knowledge, this is the first work to establish provably efficient dynamic scheduling algorithms for blockchain sharding systems.