Breaking the log n barrier on rumor spreading

TL;DR

This paper introduces a new rumor spreading algorithm that significantly improves the spreading time from logarithmic to square root of logarithm rounds in the complete graph model, even with node failures.

Contribution

It presents a novel distributed, address-oblivious algorithm using push&pull with pointer jumping that breaks the log n barrier for rumor spreading.

Findings

Spreads rumor in O() rounds with high probability.

Robust to node failures up to O(n/2^{\u0000}) nodes.

Works in a natural model with address discovery and pointer jumping.

Abstract

$O(\log n)$ rounds has been a well known upper bound for rumor spreading using push&pull in the random phone call model (i.e., uniform gossip in the complete graph). A matching lower bound of $\Omega(\log n)$ is also known for this special case. Under the assumption of this model and with a natural addition that nodes can call a partner once they learn its address (e.g., its IP address) we present a new distributed, address-oblivious and robust algorithm that uses push&pull with pointer jumping to spread a rumor to all nodes in only $O(\sqrt{\log n})$ rounds, w.h.p. This algorithm can also cope with $F= O(n/2^{\sqrt{\log n}})$ node failures, in which case all but $O(F)$ nodes become informed within $O(\sqrt{\log n})$ rounds, w.h.p.