Distributed Download from an External Data Source in Faulty Majority Settings

TL;DR

This paper develops efficient and resilient protocols for distributed data retrieval in networks with Byzantine and crash faults, optimizing query and time complexities across various communication models.

Contribution

It introduces new randomized and deterministic algorithms that achieve near-optimal query and time complexities in fault-prone distributed networks, extending previous models.

Findings

Achieves near-optimal query complexity with randomized algorithms.

Optimizes time complexity in peer-to-peer communication under dynamic adversaries.

Provides deterministic protocols with nearly optimal results in crash fault models.

Abstract

We extend the study of retrieval problems in distributed networks, focusing on improving the efficiency and resilience of protocols in the \emph{Data Retrieval (DR) Model}. The DR Model consists of a complete network (i.e., a clique) with $k$ peers, up to $\beta k$ of which may be Byzantine (for $\beta \in [0, 1)$), and a trusted \emph{External Data Source} comprising an array $X$ of $n$ bits ($n \gg k$) that the peers can query. Additionally, the peers can also send messages to each other. In this work, we focus on the Download problem that requires all peers to learn $X$. Our primary goal is to minimize the maximum number of queries made by any honest peer and additionally optimize time. We begin with a randomized algorithm for the Download problem that achieves optimal query complexity up to a logarithmic factor. For the stronger dynamic adversary that can change the set of Byzantine peers from one round to the next, we achieve the optimal time complexity in peer-to-peer communication but with larger messages. In broadcast communication where all peers (including Byzantine peers) are required to send the same message to all peers, with larger messages, we achieve almost optimal time and query complexities for a dynamic adversary. Finally, in a more relaxed crash fault model, where peers stop responding after crashing, we address the Download problem in both synchronous and asynchronous settings. Using a deterministic protocol, we obtain nearly optimal results for both query complexity and message sizes in these scenarios.