Geographic Gossip: Efficient Averaging for Sensor Networks (0709.3921v1)

Abstract: Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste in energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of $n$ and $\sqrt{n}$ respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy $\epsilon$ using $O(\frac{n^{1.5}}{\sqrt{\log n}} \log \epsilon^{-1})$ radio transmissions, which yields a $\sqrt{\frac{n}{\log n}}$ factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.

• The paper introduces a geographic gossip algorithm that reduces energy usage in sensor networks by leveraging geographic routing for efficient averaging.
• It combines geographic routing with a resampling technique to minimize redundant communications and achieve faster mixing than standard gossip protocols.
• Theoretical analysis shows that the method improves averaging efficiency by factors of n and √n in structured networks, extending sensor network lifetime.

Geographic Gossip: Efficient Averaging for Sensor Networks

The paper "Geographic Gossip: Efficient Averaging for Sensor Networks" by Dimakis, Sarwate, and Wainwright introduces and analyzes a novel gossip-based algorithm designed for distributed averaging in sensor networks. Gossip algorithms have been highlighted for their simplicity, distributed nature, and resilience in noised environments, but their efficiency is often compromised by redundant communications which lead to excess energy expenditures. The authors propose an innovative adaptation, leveraging geographic information to enhance the performance of gossip algorithms significantly.

In traditional gossip algorithms, information dissemination is akin to performing random walks over the communication graph of the sensor network. While effective, this results in slow mixing, affecting energy efficiency negatively. The proposed geographic gossip algorithm utilizes geographic routing to achieve more efficient averaging by reducing the number of required radio transmissions. This is achieved through a unique resampling technique combined with geographic routing, significantly outperforming standard gossip protocols. For structured networks like cycles and grids, geographic gossip improves efficiency by factors of $n$ and $\sqrt{n}$, respectively.

A significant contribution of this paper is its theoretical analysis, particularly in tackling random geometric graphs, a common model for wireless sensor networks with irregular topologies. The paper mathematically demonstrates that the geographic gossip algorithm computes the average to an accuracy of $\epsilon$ using $O(\frac{n^{1.5}{\sqrt{\log n} \log \epsilon^{-1})$ radio transmissions, offering a $\sqrt{\frac{n}{\log n}}$ enhancement over traditional gossip algorithms.

The implications of this research extend both practically and theoretically. For practical applications, the improvement in energy efficiency promotes longer lifetime for sensor networks critical in monitoring and data aggregation tasks. Theoretically, this work guides the exploration of further applications of geographical and structural properties of networks to improve distributed computing tasks. The method also suggests that achieving uniform distribution through geographic sampling combined with intelligent rejection techniques can overrule the potential irregular sampling bias.

Future developments in distributed algorithms could explore adaptations that use network structure knowledge to optimize other consensus problems. Additionally, other geographic routing protocols can be assessed for energy cost minimization to expand the adaptability of such algorithms across different network scenarios.

In summary, "Geographic Gossip: Efficient Averaging for Sensor Networks" encapsulates a rigorous exploration of geographical gossip techniques applied to distributed averaging, establishing quantifiable improvements over traditional methods and setting a precedent for leveraging geographic knowledge in algorithmic efficiency gains. The blending of computational efficiency with geographic strategy in this work lays a foundation for further innovations in sensor network applications, promising new inroads in minimizing energy consumption for distributed tasks.