Forwarding Without Repeating: Efficient Rumor Spreading in Bounded-Degree Graphs

TL;DR

This paper introduces FWR, a gossip protocol that efficiently spreads multiple rumors in bounded-degree graphs by preventing message repetition, significantly reducing message complexity compared to classical methods.

Contribution

The paper presents FWR, a novel rumor spreading protocol that achieves near-optimal spreading times and lower message complexity without relying on graph expansion properties.

Findings

FWR spreads rumors in near-optimal time with high probability.

FWR requires O(n) messages on bounded-degree graphs, outperforming classical forwarding.

FWR's message complexity is arbitrarily better than existing approaches even on expander graphs.

Abstract

We study a gossip protocol called forwarding without repeating (FWR). The objective is to spread multiple rumors over a graph as efficiently as possible. FWR accomplishes this by having nodes record which messages they have forwarded to each neighbor, so that each message is forwarded at most once to each neighbor. We prove that FWR spreads a rumor over a strongly connected digraph, with high probability, in time which is within a constant factor of optimal for digraphs with bounded out-degree. Moreover, on digraphs with bounded out-degree and bounded number of rumors, the number of transmissions required by FWR is arbitrarily better than that of existing approaches. Specifically, FWR requires O(n) messages on bounded-degree graphs with n nodes, whereas classical forwarding and an approach based on network coding both require {\omega}(n) messages. Our results are obtained using combinatorial and probabilistic arguments. Notably, they do not depend on expansion properties of the underlying graph, and consequently the message complexity of FWR is arbitrarily better than classical forwarding even on constant-degree expander graphs, as n \rightarrow \infty. In resource-constrained applications, where each transmission consumes battery power and bandwidth, our results suggest that using a small amount of memory at each node leads to a significant savings.