Probabilistic Counting in Uncertain Spatial Databases using Generating Functions

Location data is inherently uncertain for many reasons including 1) imprecise location measurements, 2) obsolete observations that are often interpolated, and 3) deliberate obfuscation to preserve location privacy. What makes handling uncertainty data challenging is the exponentially large number of possible worlds, which lies in O(2^N), for a database having N uncertain objects as it has been shown that general query processing in uncertain spatial data is NP-hard. Many applications using spatial data require counting the number of spatial 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 to asking whether no more than k-1 objects are located inside the circle centered at Q having a radius equal to the distance between Q and A. For this problem of counting uncertain objects within a region, an efficient solution based on Generating Functions has been proposed and successfully used in many applications, including range-count queries, kNN queries, distance ranking queries, and reverse kNN queries. This spatial gem describes the generating function technique for probabilistic counting and provides examples and implementation details.