Time Complexity vs Clause Samples
Time Complexity vs. Resilience If we define time complexity as in Section 3.4, we get the following result. In good runs, our atomic broadcast algorithms deliver messages within 2δ and require f < n/3. This result is for an atomic broadcast algorithm inspired by ▇▇▇▇▇’▇ algorithm. Similarly, we could have derived an atomic broadcast algorithm from Ben-Or’s algorithm, which would have led to a time complexity of 3δ for the delivery of messages and f < n/2. So we have the same “time complexity vs. resilience” trade-off as for consensus, see Section 3.4.
Time Complexity vs. Resilience We compare now the time complexity of the B-Consensus and the R-Consensus algorithms in “good runs.” In CDB algorithms, a good run is usually defined as a run in which no process fails and no process is falsely suspected by other processes. Here we define a good run as a run in which, for all processes p and q that do not crash, we have f irstp(1) = f irstq(1). So, contrary to the definition of good runs in the context of CDB algorithms, a good run can include process Algorithm 2 R-Consensus algorithm (f < n/3)
1: To execute propose(initV al):
Time Complexity vs. Resilience We compare now the time complexityof the B-Consensus and the R-Consensus algorithms in “good runs.” In CDB algorithms, a good run is usuallydefined as a run in which processes do not fail and are not falsely suspected by other pro- cesses. Here we define a good run as a run in which, for all correct processes p, q, we have firstp(1) = firstq(1). So, contraryto the definition of good runs in the context of CDB algorithms, a good run can include process crashes. We measure the time complexity in terms of the maximum message ▇▇- ▇▇▇ δ [2]. We assume a cost of δ for our oracle. In good runs, with Algorithm 1, every process decides after 3δ. Remember that the algorithm assumes f < n/2. In good runs, with Algorithm 2, every process decides after 2δ. The algorithm assumes f < n/3. This shows an interesting trade-off between time complexity and resilience: 3δ and f < n/2 vs. 2δ and f < n/3.