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Location data is inherently uncertain for many reasons including 1) impreciselocation measurements, 2) obsolete observations that are often interpolated,and 3) deliberate obfuscation to preserve location privacy. What makes handlinguncertainty data challenging is the exponentially large number of possibleworlds, which lies in O(2^N), for a database having N uncertain objects as ithas been shown that general query processing in uncertain spatial data isNP-hard. Many applications using spatial data require counting the number ofspatial objects within a region. An example is the k-Nearest Neighbor (kNN)query: Asking if an object A is a kNN of another object Q is equivalent toasking whether no more than k-1 objects are located inside the circle centeredat Q having a radius equal to the distance between Q and A.  For this problem of counting uncertain objects within a region, an efficientsolution based on Generating Functions has been proposed and successfully usedin many applications, including range-count queries, kNN queries, distanceranking queries, and reverse kNN queries. This spatial gem describes thegenerating function technique for probabilistic counting and provides examplesand implementation details.

Probabilistic Counting in Uncertain Spatial Databases using Generating Functions