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The P-range tree: a new data structure for range searching in secondary memory
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2-D Spatial Indexing Scheme in Optimal Time
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An asymptotically optimal multiversion B-tree
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Continuous monitoring of top-k queries over sliding windows
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Dynamic 3-Sided Planar Range Queries with Expected Doubly Logarithmic Time
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This work studies the problem of 2-dimensional searching for the 3-sided range query of the form [a, b] x (-∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers 3-sided queries in O(log n + t) worst case time and scales with O (log log n) expected with high probability update time, under continuous μ-random distributions of the x and y coordinates, where n is the current number of stored points and t is the size of the query output. Our expected update bound constitutes a considerable improvement over the O(log n) update time bound achieved by the classic Priority Search Tree of McCreight [23], as well as over the Fusion Priority Search Tree of Willard [30], which requires O(log n/log log n) time for all operations. Moreover, we externalize this solution, gaining O(logB n + t/B) worst case and O(logBlogn) amortized expected with high probability I/Os for query and update operations respectively, where B is the disk block size. Then, combining the Modified Priority Search Tree [27] with the Priority Search Tree [23], we achieve a query time of O(log log n + t) expected with high probability and an update time of O(log log n) expected with high probability, under the assumption that the x-coordinates are continuously drawn from a smooth distribution and the y-coordinates are continuously drawn from a more restricted class of distributions. The total space is linear. Finally, we externalize this solution, obtaining a dynamic data structure that answers 3-sided queries in O(logB log n + t/B) I/Os expected with high probability, and it can be updated in O(logB log n) I/Os amortized expected with high probability and consumes O(n/B) space, under the same assumptions.