## Approximate Agreement

8. dubna 2021 | Vít Zemčík | Nezařazené | Sdílet na Facebooku

The issue of the approximate agreement is not necessarily a consensus issue, but it is related to it and worth mentioning. We can change the general Byzantine problem so that each process introduces a real value instead of a binary value, and all processes must ultimately decide the actual values that lie within the other. Note that if it then corresponds to the problem of consensus with real values. Previous constructions have triggered asynchronous approximate concordance only when there may be at least 5t-1 processes, of which t can be byzantine. In this document, we conclude an open problem raised by dolev et al. 1983. We present an optimal deterministic resilience-approximate agreement algorithm that can tolerate all Byzantine errors, whereas only 3t-1 processes are needed. Thank you for joining the Simons Foundation and our generous member organizations to support arXiv during our fundraising campaign from September 23 to 27. 100% of your contribution will fund improvements and new initiatives to benefit the global scientific community of arXiv. arXivLabs is a framework that allows employees to develop and share new arXiv functions directly on our website.

The convergence rate of the algorithm and the overall complexity of the messages are effectively limited by the range of initial values of defective processes. All previous asynchronous algorithms that resist Byzantine errors may require an unlimited number of messages to send. Do you have an idea for a project that adds value to the arXiv community? Learn more about arXivLabs and how to get involved. The asynchronous algorithm is the same as the one above, except that each process waits for n-t messages, does not select the default and performs the function in the list. It is interesting to note that, although it is impossible to reach a precise consensus in a totally asynchronous system, it can be chosen to be arbitrarily small, to get closer to consensus, as desired. The synchronous algorithm basically works as follows. Each process sends its value to any other process. If a faulty process does not send a value, a default, for example.B. 0, is selected.

Each process then performs the function on the actual n values. Basically, the f function is chosen to remove the lowest t values and the highest values from the list and take the average from the rest; defective processes are therefore not in a position to influence the convergence of values. To show that it is necessary to have > 3t, accept No.3t. If all defective processes send a very high value to correct the p process, and a very low value to correct the q process, then p and q take their averages on two completely different sets of numbers, and they won`t converge. However, if no.3t-1, then p and q have a horse value on their median, and converge (very slowly) to each other. OPODIS 2004: Distributed System Principles p. 229-239 | Cite as An algorithm described by Dolev et al. [7] works by successive approximation. In other words, each cycle is closer to the goal with a guaranteed convergence rate.