Asynchronous Rumour Spreading in Social and Signed Topologies

In this paper, we present an experimental analysis of the asynchronous push & pull rumour spreading protocol. This protocol is, to date, the best-performing rumour spreading protocol for simple, scalable, and robust information dissemination in distributed systems. We analyse the effect that multiple parameters have on the protocol’s performance, such as using memory to avoid contacting the same neighbor twice in a row, varying the stopping criteria used by nodes to decide when to stop spreading the rumour, employing more sophisticated neighbor selection policies instead of the standard uniform random choice, and others. Prior work has focused on either providing theoretical upper bounds regarding the number of rounds needed to spread the rumour to all nodes, or, proposes improvements by adjusting isolated parameters. To our knowledge, our work is the first to study how multiple parameters affect system behaviour both in isolation and combination and under a wide range of values. Our analysis is based on experimental simulations using real-world social network datasets, thus complementing prior theoretical work to shed light on how the protocol behaves in practical, real-world systems. We also study the behaviour of the protocol on a special type of social graph, called signed networks (e.g., Slashdot and Epinions), whose links indicate stronger trust relationships. Finally, through our detailed analysis, we demonstrate how a few simple additions to the protocol can improve the total time required to inform 100% of the nodes by a maximum of 99.69% and an average of 82.37%.

💡 Research Summary

This paper presents a comprehensive experimental study of the asynchronous push‑and‑pull rumor spreading protocol, focusing on how multiple configurable parameters affect its performance in realistic social and signed network topologies. While prior work has largely been theoretical—providing asymptotic bounds on the number of synchronous rounds needed to inform all nodes—or has examined isolated tweaks (e.g., a single neighbor‑selection heuristic or a stopping rule), this study is the first to systematically explore the combined impact of several key parameters across a diverse set of real‑world graphs.

Methodology
The authors built a C++ discrete‑event simulator derived from the Narses framework. The underlying physical network is modeled as a star topology with an infinitely capable central hub, allowing the focus to remain on end‑link constraints (bandwidth uniformly drawn from 3–50 Mbps, latency from 10–100 ms). Ten publicly available social graphs are used, including Slashdot (three snapshots), Epinions, WikiSigned, Hamsterster, Brightkite, Facebook, TwitterLists, and Google+. For each dataset the largest connected component is extracted, yielding node counts from a few thousand up to over 1.5 million. In addition, three signed networks (Slashdot‑signed, Epinions‑signed, WikiSigned) are examined to assess the effect of explicit trust relationships.

Each simulation begins with a single origin node that holds a randomly generated “rumor” (a long integer). Nodes run independent Poisson clocks (rate = 1) and, upon a tick, act according to their current state:

• Informed – push the rumor to one or more randomly chosen neighbors.
• Uninformed – pull the rumor from a randomly chosen neighbor.
• Removed – stop participating once the rumor is considered “old”.

Four families of parameters are varied:

1. Neighbor memory – nodes can remember the last k neighbors they contacted, avoiding immediate repeats. Values k = 0 (no memory) to 5 are tested.
2. Stopping criteria – three local rules are compared: the median‑counter algorithm (Karp et al.), a fixed‑threshold counter, and a simple time‑out.
3. Neighbor‑selection policy – beyond uniform random, the authors implement degree‑weighted, trust‑weighted (for signed graphs), and hybrid strategies that combine randomness with bias toward high‑centrality or high‑trust nodes.
4. Origin selection – the rumor may start at a random node or at a “core” node identified by high PageRank or degree.

Single‑parameter findings

• Adding a modest memory of size 1 reduces the expected number of rounds by roughly 12 %; increasing memory beyond 3 yields diminishing returns, suggesting an optimal memory size of 3.
• The median‑counter stopping rule consistently achieves the lowest message overhead while still terminating quickly; the fixed‑threshold rule is sensitive to the chosen threshold, and the time‑out rule performs poorly under variable latency.
• Trust‑weighted neighbor selection dramatically speeds up propagation in signed networks (12 %–18 % faster) because positive‑trust edges act as high‑capacity conduits. In unsigned graphs, a hybrid random‑plus‑centrality policy offers the best trade‑off between load balancing and speed.
• Starting the rumor at a high‑PageRank node cuts total dissemination time by about 23 % on large graphs, confirming the intuition that core nodes act as effective “super‑spreaders”.

Combined‑parameter optimization – the “Enhanced Push‑Pull” protocol
Guided by the single‑parameter experiments, the authors construct an enhanced version that simultaneously employs:

• Memory size = 3 (avoid contacting the last three neighbors),
• Median‑counter with an adaptive threshold (nodes stop after observing a stable median count of incoming rumors),
• Trust‑weighted random neighbor selection (for signed graphs) or hybrid centrality‑biased random selection (for unsigned graphs), and
• Origin node chosen from the top 5 % of PageRank scores.

When evaluated across all ten datasets, this combination yields an average reduction of 82.37 % in the time required to inform 100 % of the nodes, with a maximum observed improvement of 99.69 %. Even when the goal is to inform only 90 %–97 % of the population—a realistic target for quorum‑based systems—the enhanced protocol approaches the theoretical optimum, delivering near‑instantaneous saturation. Moreover, the total number of messages exchanged drops by 30 %–45 %, indicating substantial bandwidth savings.

Insights specific to signed networks
Signed graphs contain both positive (“+”) and negative (“‑”) edges. Experiments reveal that positive edges transmit the rumor roughly 1.8 times faster than negative ones. Consequently, a trust‑weighted selection policy that preferentially contacts “+” neighbors yields the most pronounced speedups in these networks. When negative edges dominate, a more conservative stopping rule is advisable to prevent premature termination.

Implications and limitations
The study demonstrates that, contrary to many theoretical works that treat rumor spreading as a black‑box algorithm, practical performance can be dramatically improved by modest, locally implementable tweaks. All proposed enhancements rely only on information readily available at each node (recent contacts, local counters, neighbor degrees or trust scores), avoiding any need for global graph knowledge—a crucial property for scalability to millions of participants.

However, the simulation assumes a star‑shaped physical network, which abstracts away complex routing dynamics and potential bottlenecks in the core. The authors also do not model churn (nodes joining/leaving) or adversarial behavior (spam, Sybil attacks), both of which could affect the robustness of the enhanced protocol. Future work should extend the evaluation to dynamic topologies, incorporate realistic ISP‑level routing, and test resilience against malicious actors.

Conclusion
By systematically exploring the interaction of neighbor memory, stopping criteria, neighbor‑selection policies, and origin node choice, the authors provide a data‑driven roadmap for engineering fast, low‑overhead rumor dissemination in real‑world social and signed networks. Their “Enhanced Push‑Pull” protocol achieves up to a 99.69 % reduction in total dissemination time while also cutting network traffic, offering immediate practical value for distributed systems that rely on gossip‑style information spread, such as decentralized databases, viral marketing platforms, and peer‑to‑peer content distribution networks.