Spatially-decaying aggregation over a network

Abstract

Data items are often associated with a location in which they are present or collected, and their relevance or influence decays with their distance. Aggregate values over such data thus depend on the observing location, where the weight given to each item depends on its distance from that location. We term such aggregation spatially-decaying. Spatially-decaying aggregation has numerous applications: Individual sensor nodes collect readings of an environmental parameter such as contamination level or parking spot availability; the nodes then communicate to integrate their readings so that each location obtains contamination level or parking availability in its neighborhood. Nodes in a p2p network could use a summary of content and properties of nodes in their neighborhood in order to guide search. In graphical databases such as Web hyperlink structure, properties such as subject of pages that can reach or be reached from a page using link traversals provide information on the page. We formalize the notion of spatially-decaying aggregation and develop efficient algorithms for fundamental aggregation functions, including sums and averages, random sampling, heavy hitters, quantiles, and L p norms.