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DOI: 10.4230/LIPIcs.FSTTCS.2015.336
URN: urn:nbn:de:0030-drops-56488
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5648/
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Bishnu, Arijit ; Chakrabarti, Amit ; Nandy, Subhas C. ; Sen, Sandeep

On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model

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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 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.

BibTeX - Entry

@InProceedings{bishnu_et_al:LIPIcs:2015:5648,
  author =	{Arijit Bishnu and Amit Chakrabarti and Subhas C. Nandy and Sandeep Sen},
  title =	{{On Density, Threshold and Emptiness Queries for Intervals in the Streaming Model}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{336--349},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Prahladh Harsha and G. Ramalingam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5648},
  URN =		{urn:nbn:de:0030-drops-56488},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.336},
  annote =	{Keywords: Density, threshold, emptiness queries, interval queries, streaming model, heavy hitter, frequency estimation}
}

Keywords: Density, threshold, emptiness queries, interval queries, streaming model, heavy hitter, frequency estimation
Seminar: 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)
Issue Date: 2015
Date of publication: 11.12.2015


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