Dynamic reduction algorithms for fault tolerant convergent voting with hybrid faults

• Authors: Roger M. Kieckhafer;Paul J. Weber
• Venue: Dynamic reduction algorithms for fault tolerant convergent voting with hybrid faults
• Year: 2006

Many fault-tolerant systems require distributed algorithms that guarantee non-faulty processes agree on a shared value in the presence of faults. For many applications, such as clock synchronization and numerical data voting, processes do not have to agree exactly. Instead, it is sufficient for all non-faulty processes to satisfy the criterion of Approximate Agreement in which processes must only agree within some predetermined tolerance. One method of achieving Approximate Agreement is through the utilization of convergent voting algorithms. Previous research analyzed convergent voting algorithms in the context of hybrid fault models. The Omissive/Transmissive Hybrid Five-Mode Fault Model (OTH-5) presented by Kieckhafer and Azadmanesh partitioned symmetric and asymmetric faults each according to transmissive or omissive behavior. This dissertation presents a new fault model named the Omissive/Transmissive Hybrid Six-Mode Fault Model (OTH-6) in which the most severe fault mode of the OTH-5 fault model, the Transmissive Asymmetric fault mode, is partitioned into two submodes: the Single Error Omissive Asymmetric and the Fully Transmissive Asymmetric fault mode. The advantage of such partitioning is that Fully Transmissive Asymmetric faults now encompass all faults that are implausible in a broadcast-based system. Furthermore, we present a new family of Omission-Mean-Subsequence-dynamically-Reduced (OMSdR) algorithms which exploit the partitioning of the OTH-6 Fault Model. The algorithms introduce a fundamental shift in the approach of convergent voting algorithms by allowing distinct nodes to discard different values for the same voting round. By leveraging this enhancement, we then prove that OMSdR algorithms are the first convergent voting algorithms that achieve a fault-tolerance bound of a strict one-half majority rather than a two-thirds super majority of non-faulty processes for all plausible fault scenarios.