📝 SummarXiv

Abstract

The distributedData Retrieval (DR) model consists of $k$ peers connected by a complete peer-to-peer communication network, and a trusted external data source that stores an array $\textbf{X}$ of $n$ bits ($n \gg k$). Up to $\beta k$ of the peers might fail in any execution (for $\beta \in [0, 1)$). Peers can obtain the information either by inexpensive messages passed among themselves or through expensive queries to the source array $\textbf{X}$. In the DR model, we focus on designing protocols that minimize the number of queries performed by any nonfaulty peer (a measure referred to as query complexity) while maximizing the resilience parameter $\beta$. The Download problem requires each nonfaulty peer to correctly learn the entire array $\textbf{X}$. Earlier work on this problem focused on synchronous communication networks and established several deterministic and randomized upper and lower bounds. Our work is the first to extend the study of distributed data retrieval to asynchronous communication networks. We address the Download problem under both the Byzantine and crash failure models. We present query-optimal deterministic solutions in an asynchronous model that can tolerate any fixed fraction $\beta<1$ of crash faults. In the Byzantine failure model, it is known that deterministic protocols incur a query complexity of $\Omega(n)$ per peer, even under synchrony. We extend this lower bound to randomized protocols in the asynchronous model for $\beta \geq 1/2$, and further show that for $\beta < 1/2$, a randomized protocol exists with near-optimal query complexity. To the best of our knowledge, this is the first work to address the Download problem in asynchronous communication networks.