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The moving k nearest neighbor (MkNN) query finds the k nearest neighbors of a moving query point continuously. The high potential of reducing the query processing cost as well as the large spectrum of associated applications have attracted considerable attention to this query type from the database community. This paper presents an incremental safe-region-based technique for answering MkNN queries, called the V*-Diagram. In general, a safe region is a set of points where the query point can move without changing the query answer. Traditional safe-region approaches compute a safe region based on the data objects but independent of the query location. Our approach exploits the current knowledge of the query point and the search space in addition to the data objects. As a result, the V*-Diagram has much smaller IO and computation costs than existing methods. The experimental results show that the V …