Simple and Optimal Randomized Fault-Tolerant Rumor Spreading

TL;DR

This paper introduces simple, randomized protocols for rumor spreading in fully connected networks that are fault-tolerant, message-efficient, and operate optimally in logarithmic time without synchronization or prior failure estimates.

Contribution

It presents the first protocols combining linear message complexity, adversarial fault tolerance, and optimal runtime in a fully connected network setting.

Findings

Protocols achieve $O( ext{log } n)$ runtime with high probability.

Use only push-operations without synchronization or initial wake-up.

Require a linear number of messages and tolerate arbitrary node failures.

Abstract

We revisit the classic problem of spreading a piece of information in a group of $n$ fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasienic and Pelc (1996), we derive for the first time protocols that (i) use a linear number of messages, (ii) are correct even when an arbitrary number of adversarially chosen processors does not participate in the process, and (iii) with high probability have the asymptotically optimal runtime of $O(\log n)$ when at least an arbitrarily small constant fraction of the processors are working. In addition, our protocols do not require that the system is synchronized nor that all processors are simultaneously woken up at time zero, they are fully based on push-operations, and they do not need an a priori estimate on the number of failed nodes. Our protocols thus overcome the typical disadvantages of the two known approaches, algorithms based on random gossip (typically needing a large number of messages due to their unorganized nature) and algorithms based on fair workload splitting (which are either not {time-efficient} or require intricate preprocessing steps plus synchronization).