2026-09-13T04:32:33Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24877 2026-09-05T19:00:16Z ddc:004 open_access

Brief Announcement: Asynchronous Approximate Agreement with Quadratic Communication Mizrahi Erbes, Mose Wattenhofer, Roger Approximate agreement byzantine fault tolerance communication complexity We consider an asynchronous network of n message-sending parties, up to t of which are byzantine. We study approximate agreement, where the parties obtain approximately equal outputs in the convex hull of their inputs. In their seminal work, Abraham, Amit and Dolev [OPODIS '04] solve this problem in ℝ with the optimal resilience t < n/3 with a protocol where each party reliably broadcasts a value in every iteration. This takes Θ(n²) messages per reliable broadcast, or Θ(n³) messages per iteration. In this work, we forgo reliable broadcast to achieve asynchronous approximate agreement against t < n/3 faults with quadratic communication. In a tree with the maximum degree Δ and the centroid decomposition height h, we achieve edge agreement in at most 6h + 1 rounds with 𝒪(n²) messages of size 𝒪(log Δ + log h) per round. We do this by designing a 6-round multivalued 2-graded consensus protocol and using it to recursively reduce the task to edge agreement in a subtree with a smaller centroid decomposition height. Then, we achieve edge agreement in the infinite path ℤ, again with the help of 2-graded consensus. Finally, we show that our edge agreement protocol enables ε-agreement in ℝ in 6log₂M/(ε) + 𝒪(log log M/(ε)) rounds with 𝒪(n² log M/(ε)) messages and 𝒪(n²log M/(ε)log log M/(ε)) bits of communication, where M is the maximum non-byzantine input magnitude. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mose Mizrahi Erbes and Roger Wattenhofer 2025 Is Part Of LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2025.61 urn:nbn:de:0030-drops-248771 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.61 eng https://creativecommons.org/licenses/by/4.0/legalcode