On the Efficiency of Dynamic Transaction Scheduling in Blockchain Sharding

TL;DR

This paper introduces new dynamic scheduling algorithms for blockchain sharding systems, achieving near-optimal latency bounds in both stateless and stateful models, and proves the computational hardness of optimal scheduling approximation.

Contribution

It presents the first provably efficient dynamic scheduling algorithms for blockchain sharding, with competitive ratios close to the theoretical lower bounds.

Findings

Achieves $O(d \, \log^2 s \cdot \min\{k, \sqrt{s}\})$ competitive ratio in stateless model.

Achieves $O(\log s \cdot \min\{k, \sqrt{s}\} + \log^2 s)$ competitive ratio in stateful model.

Proves NP-hardness of approximating optimal schedules within a certain factor.

Abstract

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.