Fractionally cascaded information in a sensor network

We address the problem of distributed information aggregation and storage in a sensor network, where queries can be injected anywhere in the network. The principle we propose is that a sensor should know a "fraction" of the information from distant parts of the network, in an exponentially decaying fashion by distance. We show how a sampled scalar field can be stored in this distributed fashion, with only a modest amount of additional storage and network traffic. Our storage scheme makes neighboring sensors have highly correlated world views; this allows smooth information gradients and enables local search algorithms to work well. We study in particular how this principle of fractionally cascaded information can be exploited to answer range queries about the sampled field efficiently. Using local decisions only we are able to route the query to exactly the portions of the field where the sought information is stored. We provide a rigorous theoretical analysis showing that our scheme is close to optimal.