Blockchains facilitate decentralization, security, identity, and data management in cyber-physical systems. However, consensus protocols used in blockchains are prone to high message and computational complexity costs and are not suitable to be used in IoT. One way to reduce message complexity is to randomly assign network nodes into committees or shards. Keeping committee sizes small is then desirable in order to achieve lower message complexity, but this comes with a penalty of reduced reliability as there is a higher probability that a large number of faulty nodes will end up in a committee. In this work, we study the problem of estimating a probability of a failure in randomly sharded networks. We provide new results and improve existing bounds on the failure probability. Thus, our framework also paves the way to reduce committee sizes without reducing reliability.
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