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Dynamic Group Management to Improve the Scalability of PBFT
Jinsung Cho, Gwangyong Kim, Geunmo Kim, Bongjae Kim, Min Choi
http://doi.org/10.5626/JOK.2023.50.5.369
A consensus algorithm that affects the reliability and performance of a blockchain is used for identical decision-making of nodes participating in the consensus. PBFT(Practical Byzantine Falut Tolerance) is a voting-based consensus algorithm with an O(n2) time complexity. The scalability of PBFT is generally poor. This paper proposes a scheme for grouping the nodes participating in a PBFT-based blockchain network and dynamically managing each group by layering it. In addition, we create a mathematical model for estimating the expected time required for consensus of the proposed scheme. Afterwards, we propose a dynamic consensus algorithm for dynamically adjusting the structures of groups and layers based on the model for estimating the expected time of a consensus. As a result of the experiment, the proposed scheme improves the performance of the consensus time by about 97% on average compared to the group-based PBFT without hierarchical structures.
Parallel Algorithms for Finding Consensus of Circular Strings
The consensus problem is finding a representative string, called a consensus, of a given set S of k strings. Circular strings are different from linear strings in that the last symbol precedes the first symbol. Given a set S of circular strings of length n over an alphabet ∑ , we first present an O(｜∑｜nlogn) time parallel algorithm for finding a consensus of S minimizing both radius and distance sum when k=3 using O(n) threads. Then we present an O(｜∑｜n²logn) time parallel algorithm for finding a consensus of S minimizing distance sum when k=4 using O(n) threads. Finally, we compare execution times of our algorithms implemented using CUDA with corresponding sequential algorithms.
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