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I/OEfficient Data Structures for Colored Range and Prefix Reporting
"... Motivated by information retrieval applications, we consider the onedimensional colored range reporting problem in rank space. The goal is to build a static data structure for sets C1,..., Cm ⊆ {1,..., σ} that supports queries of the kind: Given indices a, b, report the set ⋃ a≤i≤b Ci. We study the ..."
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Motivated by information retrieval applications, we consider the onedimensional colored range reporting problem in rank space. The goal is to build a static data structure for sets C1,..., Cm ⊆ {1,..., σ} that supports queries of the kind: Given indices a, b, report the set ⋃ a≤i≤b Ci. We study the problem in the I/O model, and show that there exists an optimal linearspace data structure that answers queries in O(1 + k/B) I/Os, where k denotes the output size and B the disk block size in words. In fact, we obtain the same bound for the harder problem of threesided orthogonal range reporting. In this problem, we are to preprocess a set of n twodimensional points in rank space, such that all points inside a query rectangle of the form [x1, x2]×(−∞, y] can be reported. The best previous bounds for this problem is either O(n lg 2 B n) space and O(1 + k/B) query I/Os, or O(n) space and O(lg (h) B n + k/B) query I/Os, where lg(h)
Efficient Processing of 3Sided Range Queries with Probabilistic Guarantees
"... This work studies the problem of 2dimensional searching for the 3sided range query of the form [a, b] × (−∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers 3sided queries in O(log n + t) worst ..."
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This work studies the problem of 2dimensional searching for the 3sided range query of the form [a, b] × (−∞, c] in both main and external memory, by considering a variety of input distributions. A dynamic linear main memory solution is proposed, which answers 3sided queries in O(log n + t) worst case time and scales with O(log log n) expected with high probability update time, under continuous µrandom 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 log n