External Memory Three-Sided Range Reporting and Top-k Queries with Sublogarithmic Updates

An external memory data structure is presented for maintaining a dynamic set of N two-dimensional points under the insertion and deletion of points, and supporting unsorted 3-sided range reporting queries and top-k queries, where top-k queries report the k points with highest y-value within a given x-range. For any constant 0 < epsilon <= 1/2, a data structure is constructed that supports updates in amortized O(1/epsilon B(1-s)log(B)N) IOs and queries in amortized O(1/epsilon log(B)N K/B) IOs, where B is the external memory block size, and K is the size of the output to the query (for top-k queries K is the minimum of k and the number of points in the query interval). The data structure uses linear space. The update bound is a significant factor B1-epsilon improvement over the previous best update bounds for these two query problems, while staying within the same query and space bounds.