Consensus without failures A set of n nodes each holding an input value viE(0,1}, all nodes need to output an identical out value that is some vi. How to solve this problem when there is no failure? Execute at each node i: 0ut←-Vi: Send out to all nodes. Wait until receive all messages sent in this round. out -min of received values,and current out. Output out as final decision. Clearly this algorithm achieves termination,agreement,and validity. This algorithm needs 1 round,sends (n2)messages in total. Consensus without failures • A set of 𝑛 nodes each holding an input value 𝑣𝑖 ∈ 0,1 , all nodes need to output an identical 𝑜𝑢𝑡 value that is some 𝑣𝑖 . • How to solve this problem when there is no failure? 0 1 1 Execute at each node 𝒊: 𝑜𝑢𝑡 ← 𝑣𝑖 . Send 𝑜𝑢𝑡 to all nodes. Wait until receive all messages sent in this round. 𝑜𝑢𝑡 ← min of received values, and current 𝑜𝑢𝑡. Output 𝑜𝑢𝑡 as final decision. 0 1 1 Clearly this algorithm achieves termination, agreement, and validity. This algorithm needs 1 round, sends Θ 𝑛 2 messages in total