Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust message-passing schemes for distributed information processing over networks. However for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges as slowly as flooding ($O(n^2)$ messages).
A recently proposed algorithm called geographic gossip improves gossip efficiency by a $\sqrt{n}$ factor, by exploiting geographic information to enable multi-hop long distance communications. In this paper we prove that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional $\sqrt{n}$ factor and is order optimal ($O(n)$ messages) for grids and random geometric graphs.
We develop a general technique (travel agency method) based on Markov chain mixing time inequalities, which can give bounds on the performance of randomized message-passing algorithms operating over various graph topologies.
Generalized Geometric Programming for Rate Allocation in Consensus
分布式平均（英语：Distributed average），或分布式平均共识（英语：Distributed average consensus），是一种计算分散在网络节点中的数据样本均值的常用方法。通过与邻居迭代地交换消息，网络的节点可以收敛到其初始状态的样本均值的一致性。在实际场景中，这些消息受到带宽和功率约束，这促使设计有损压缩策略。很少有现有的工作考虑的角度来看，约束优化，这提供了一个原则性的方法，设计的有损压缩计划的速率分配问题，允许放宽某些假设，并提供性能保证。我们表明，高斯分布的初始状态与熵编码的标量量化和矢量量化的编码率分布平均可以通过广义几何规划进行优化。在没有来自过去状态的边信息的情况下，该方法找到在有限运行时间内实现目标均方误差所需的最小化聚合编码速率的节点和迭代上的速率分配。我们的速率分配相比，通过数值模拟的一些现有技术。结果激励边信息通过差分或预测编码，以提高率失真性能的结合。
