Byzantine Agreement (BA) is a key component in many distributed systems. While Dolev and Reischuk have proven a long time ago that quadratic communication complexity is necessary for worst-case runs, the question of what can be done in practically common runs with fewer failures remained open. In this paper we present the first Byzantine Broadcast algorithm with O(n(f+1)) communication complexity in a model with resilience of n = 2t+1, where 0 ≤ f ≤ t is the actual number of process failures in a run. And for BA with strong unanimity, we present the first optimal-resilience algorithm that has linear communication complexity in the failure-free case and a quadratic cost otherwise.
@InProceedings{cohen_et_al:LIPIcs.OPODIS.2022.18, author = {Cohen, Shir and Keidar, Idit and Spiegelman, Alexander}, title = {{Make Every Word Count: Adaptive Byzantine Agreement with Fewer Words}}, booktitle = {26th International Conference on Principles of Distributed Systems (OPODIS 2022)}, pages = {18:1--18:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-265-5}, ISSN = {1868-8969}, year = {2023}, volume = {253}, editor = {Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.18}, URN = {urn:nbn:de:0030-drops-176385}, doi = {10.4230/LIPIcs.OPODIS.2022.18}, annote = {Keywords: Byzantine Agreement, Byzantine Broadcast, Adaptive communication} }
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