Direction-Reversing Quasi-Random Rumor Spreading with Restarts

TL;DR

This paper introduces a direction-reversing element with restarts to an existing quasi-random rumor spreading protocol, significantly reducing randomness while maintaining broadcast efficiency.

Contribution

It proposes a novel hybrid protocol with direction reversal and restarts, improving efficiency over previous models with less randomness.

Findings

Achieves the same broadcast time with fewer random choices.

Provides a constant factor improvement over the hybrid protocol.

Reduces randomness by roughly half while maintaining performance.

Abstract

In a recent work, Doerr and Fouz [\emph{Asymptotically Optimal Randomized Rumor Spreading}, in ArXiv] present a new quasi-random PUSH algorithm for the rumor spreading problem (also known as gossip spreading or message propagation problem). Their \emph{hybrid protocol} outperforms all known PUSH protocols. In this work, we add to the hybrid protocol a direction-reversing element. We show that this \emph{direction-reversing quasi-random rumor spreading protocol with random restarts} yields a constant factor improvement over the hybrid model, if we allow the same dose of randomness. Put differently, our protocol achieves the same broadcasting time as the hybrid model by employing only (roughly) half the number of random choices.