Parameter-independent Iterative Approximate Byzantine Consensus

In this work, we explore iterative approximate Byzantine consensus algorithms that do not make explicit use of the global parameter of the graph, i.e., the upper-bound on the number of faults, f.

💡 Research Summary

The paper addresses a fundamental limitation of existing iterative approximate Byzantine consensus (IABC) algorithms: their reliance on a globally known fault bound f, the maximum number of Byzantine nodes the system is expected to tolerate. In many real‑world distributed systems—such as blockchain networks, autonomous vehicle fleets, and large‑scale IoT deployments—the exact value of f is either unknown or subject to change as nodes join, leave, or become compromised. Over‑estimating f reduces performance, while under‑estimating f can break safety guarantees, causing divergence or incorrect consensus. To overcome this, the authors propose a parameter‑independent IABC (PIABC) algorithm that requires no prior knowledge of f and instead adapts its behavior solely on locally observed information.

System Model

The system is modeled as an undirected communication graph G(V,E) with n nodes. Up to b nodes may behave Byzantine, where b is the actual (unknown) number of faulty processes. Communication proceeds in synchronous rounds: each correct node broadcasts its current state x_i(t) to all neighbors, receives a multiset of values from its neighbor set N_i, and then computes a new state x_i(t+1). The goal is approximate agreement: all correct nodes’ values must converge to a common interval of bounded width, despite Byzantine interference.

Core Algorithmic Ideas

PIABC replaces the classic “trim‑f” operation (which discards the f largest and f smallest received values) with a dynamic trimming mechanism that determines how many extreme values to discard based on the observed distribution of the received messages. The algorithm proceeds as follows for each node i in every round t:

1. Sort Received Values – The node orders the values received from N_i in ascending order.
2. Compute Adaptive Trimming Ratio τ_i(t) – Using the local variance σ_i(t) and median m_i(t) of the sorted list, the node calculates a trimming proportion
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