A Distributed Routing Algorithm for Internet-wide Geocast

Geocast is the concept of sending data packets to nodes in a specified geographical area instead of nodes with a specific address. To route geocast messages to their destination we need a geographic routing algorithm that can route packets efficiently to the devices inside the destination area. Our goal is to design an algorithm that can deliver shortest path tree like forwarding while relying purely on distributed data without central knowledge. In this paper, we present two algorithms for geographic routing. One based purely on distance vector data, and one more complicated algorithm based on path data. In our evaluation, we show that our purely distance vector based algorithm can come close to shortest path tree performance when a small number of routers are present in the destination area. We also show that our path based algorithm can come close to the performance of a shortest path tree in almost all geocast situations

Geographic Gossip: Efficient Averaging for Sensor Networks

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.Comment: To appear, IEEE Transactions on Signal Processin