文章基本信息

标题：On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model
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作者：Arijit Bishnu ; Amit Chakrabarti ; Subhas C. Nandy 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：45
页码：336-349
DOI：10.4230/LIPIcs.FSTTCS.2015.336
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In this paper, we study the maximum density, threshold and emptiness queries for intervals in the streaming model. The input is a stream S of n points in the real line R and a floating closed interval W of width alpha. The specific problems we consider in this paper are as follows. - Maximum density: find a placement of W in R containing the maximum number of points of S. - Threshold query: find a placement of W in R, if it exists, that contains at least Delta elements of S. - Emptiness query: find, if possible, a placement of W within the extent of S so that the interior of W does not contain any element of S. The stream S, being huge, does not fit into main memory and can be read sequentially at most a constant number of times, usually once. The problems studied here in the geometric setting have relations to frequency estimation and heavy hitter identification in a stream of data. We provide lower bounds and results on trade-off between extra space and quality of solution. We also discuss generalizations for the higher dimensional variants for a few cases.
关键词：Density; threshold; emptiness queries; interval queries; streaming model; heavy hitter; frequency estimation