Computing in a Faulty Congested Clique

TL;DR

This paper investigates the Faulty Congested Clique model, demonstrating that many problems can be solved efficiently despite adversarial node failures, by transforming algorithms from the non-faulty to the faulty setting with minimal overhead.

Contribution

It introduces a method to adapt non-faulty Congested Clique algorithms to the faulty model with small overhead, maintaining efficiency even with many node failures.

Findings

Tasks of O(n log n) bits per node are solvable in roughly n rounds despite faults.

The approach preserves the complexity of semi-ring matrix multiplication up to polylog factors in the faulty model.

The method applies even when an adversary causes failures of up to 99% of nodes.

Abstract

We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of $O(n\log{n})$-bit input per node can be solved in roughly $n$ rounds, where $n$ is the size of the network. This nearly matches the linear upper bound on the complexity of the non-faulty Congested Clique model for such problems, by learning the entire input, and it holds in the faulty model even with a linear number of faults. Our main contribution is that we establish that one can do much better by looking more closely at the computation. Given a deterministic algorithm $\mathcal{A}$ for the non-faulty Congested Clique model, we show how to transform it into an algorithm $\mathcal{A}'$ for the faulty model, with an overhead that could be as small as some logarithmic-in-$n$ factor, by considering refined complexity measures of $\mathcal{A}$. As an exemplifying application of our approach, we show that the $O(n^{1/3})$-round complexity of semi-ring matrix multiplication [Censor-Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela, PODC 2015] remains the same up to polylog factors in the faulty model, even if the adversary can fail $99\%$ of the nodes (or any other constant fraction).