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On density, threshold and emptiness queries for intervals in the streaming model
A. Bishnu, A. Chakrabarti, S.C. Nandy,
Published in Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
2015
Volume: 45
   
Pages: 336 - 349
Abstract
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 α. 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 Δ 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. © Arijit Bishnu, Amit Chakrabarti, Subhas C. Nandy, and Sandeep Sen;.
About the journal
Published in Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Open Access
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