Finding One-Of Probably Nearest Neighbors with Minimum Location Updates

Abstract—Location information is necessarily uncertain when objects are constantly moving. The cost can be high to maintain precise locations at the application server for all the objects while many applications may not need all the costly precision that is technically possible. An interesting question is how to reduce the cost associated with obtaining precise locations while satisfying user requirements. A general technique of maintaining uncertain location information is using a “safe-region ” for each object, a region in which the object must be in but it is not known where it exactly is. Location updates are only needed when the object moves out of its safe region, or a user query needs more precise information to answer. This paper uses the same idea for finding an object that is likely to be the nearest neighbor of a query location, a query type termed herein Probabilistic one-of Nearest Neighbor (PoNN) query. An algorithm is described that first tries to answer a given PoNN query with the known safe regions. If this fails, the algorithm selects some objects to ask for their precise locations (called location exposures). An innovative method is used by the algorithm in deciding which objects to expose in order to reduce the total number of exposures. The innovation includes an information gain formulation of the problem and careful probability calculations. The paper details the algorithm and shows an experimental study of the algorithm against more straightforward solutions in a simulated environment. I