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DOI: 10.4230/LIPIcs.CPM.2016.3

Encoding Two-Dimensional Range Top-k Queries

Authors: Seungbum Jo, Rahul Lingala, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract

We consider various encodings that support range top-k queries on a two-dimensional array containing elements from a total order. For an m x n array, we first propose an almost optimal encoding for answering one-sided top-k queries, whose query range is restricted to [1 ... m][1 .. a], for 1 <= a <= n. Next, we propose an encoding for the general top-k queries that takes m^2 * lg(binom((k+1)n)(n)) + m * lg(m) + o(n) bits. This generalizes the one-dimensional top-k encoding of Gawrychowski and Nicholson [ICALP, 2015]. Finally, for a 2 x n array, we obtain a 2 lg(binom(3n)(n)) + 3n + o(n)-bit encoding for answering top-2 queries.

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Seungbum Jo, Rahul Lingala, and Srinivasa Rao Satti. Encoding Two-Dimensional Range Top-k Queries. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 3:1-3:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jo_et_al:LIPIcs.CPM.2016.3,
  author =	{Jo, Seungbum and Lingala, Rahul and Satti, Srinivasa Rao},
  title =	{{Encoding Two-Dimensional Range Top-k Queries}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{3:1--3:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.3},
  URN =		{urn:nbn:de:0030-drops-60704},
  doi =		{10.4230/LIPIcs.CPM.2016.3},
  annote =	{Keywords: Encoding model, top-k query, range minimum query}
}

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Encoding Two-Dimensional Range Top-k Queries

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