Bishnu, Arijit
[VerfasserIn];
Chakrabarti, Amit
[VerfasserIn];
Nandy, Subhas C.
[VerfasserIn];
Sen, Sandeep
[VerfasserIn]
;
Arijit Bishnu and Amit Chakrabarti and Subhas C. Nandy and Sandeep Sen
[MitwirkendeR]
On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model
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Beschreibung:
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.