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The Blockchain technology, featured with its decentralized tamper-resistance based on a Peer-to-Peer network, has been widely applied in financial applications, and even further been extended to industrial applications. However, the weak scalability of traditional Blockchain technology severely affects the wide adoption due to the well-known trillema of decentralization-security-scalability in Blockchains. In regards to this issue, a number of solutions have been proposed, targeting to boost the scalability while preserving the decentralization and security. They range from modifying the on-chain data structure and consensus algorithms to adding the off-chain technologies. Therein, one of the most practical methods to achieve horizontal scalability along with the increasing network size is sharding, by partitioning network into multiple shards so that the overhead of duplicating communication, storage, and computation in each full node can be avoided. This paper presents a survey focusing on sharding in Blockchains in a systematic and comprehensive way. We provide detailed comparison and quantitative evaluation of major sharding mechanisms, along with our insights analyzing the features and restrictions of the existing solutions. We also provide theoretical upper-bound of the throughput for each considered sharding mechanism. The remaining challenges and future research directions are also reviewed.

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Link scheduling plays a key role in the network capacity and the transmission delay. In this paper, we study the problem of maximum link scheduling (MLS), aiming to characterize the maximum number of links that can be successfully scheduled simultaneously under Rayleigh-fading and multiuser interference. After analyzing the minimum distance between successful links in the existing GHW scheduling algorithm, we propose a DLS (Distance-based Link Scheduling) algorithm. Then, the global interference is characterized and bounded by introducing a separation distance between selected links, building on which we propose a distributed version of DLS (denoted by DDLS) that converges to a constant factor of the non-fading optimum within time complexity O(n ln n), where n is the number of links. Furthermore, we study the Shortest Link Scheduling (SLS) problem, which minimizes the number of time slots to successfully schedule each link for at least once. An algorithm for SLS with approximation factor of O(ln n) is obtained by executing DDLS. Extensive simulations show that DDLS greatly outperforms GHW and the other two popular algorithms.

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