Quasirandom Rumor Spreading

TL;DR

This paper introduces a quasirandom variant of rumor spreading that maintains the efficiency of the classical randomized model, with some cases showing improved bounds, across various network types.

Contribution

It proposes and analyzes a quasirandom rumor spreading model that preserves or improves upon classical dissemination bounds across different graph families.

Findings

Same O(log n) spreading time as classical model on various graphs

In some cases, quasirandom model achieves better bounds

Performance is robust to neighbor list orderings

Abstract

We propose and analyze a quasirandom analogue of the classical push model for disseminating information in networks ("randomized rumor spreading"). In the classical model, in each round each informed vertex chooses a neighbor at random and informs it, if it was not informed before. It is known that this simple protocol succeeds in spreading a rumor from one vertex to all others within O(log n) rounds on complete graphs, hypercubes, random regular graphs, Erdos-Renyi random graph and Ramanujan graphs with probability 1-o(1). In the quasirandom model, we assume that each vertex has a (cyclic) list of its neighbors. Once informed, it starts at a random position on the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above-mentioned bounds still hold. In some cases, even better bounds than for the classical model can be shown.