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• W1986297550 abstract "We study the following problem: Given an array A storing N real numbers, preprocess it to allow fast reporting of the K smallest elements in the subarray A[i, j] in sorted order, for any triple (i, j, K) with 1 ≤ i ≤ j ≤ N and 1 ≤ K ≤ j − i + 1. We are interested in scenarios where the array A is large, necessitating an I/O-efficient solution.For a parameter f with 1 ≤ f ≤ logmn, we construct a data structure that uses O((N/f) logmn) space and achieves a query bound of O(logBN + fK/B) I/Os, where B is the block size, M is the size of the main memory, n:= N/B, and m:= M/B. Our main contribution is to show that this solution is nearly optimal. To be precise, we show that achieving a query bound of O(logαn + fK/B) I/Os, for any constant α, requires Ω(Nf−1 logMn/log(f−1 logMn)) space, assuming B = Ω(log N). For M ≥ B1+e, this is within a log logmn factor of the upper bound. The lower bound assumes indivisibility of records and holds even if we assume K is always set to j − 1 + 1.We also show that it is the requirement that the K smallest elements be reported in sorted order which makes the problem hard. If the K smallest elements in the query range can be reported in any order, then we can obtain a linear-size data structure with a query bound of O(logBN + K/B) I/Os." @default.
• W1986297550 created "2016-06-24" @default.
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• W1986297550 date "2011-01-23" @default.
• W1986297550 modified "2023-09-29" @default.
• W1986297550 title "Ordered and unordered top-K range reporting in large data sets" @default.
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• W1986297550 doi "https://doi.org/10.5555/2133036.2133067" @default.
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