License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.92
URN: urn:nbn:de:0030-drops-61936
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6193/
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Grønlund, Allan ; Larsen, Kasper Green

Towards Tight Lower Bounds for Range Reporting on the RAM

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LIPIcs-ICALP-2016-92.pdf (0.5 MB)

Abstract

In the orthogonal range reporting problem, we are to preprocess a set of n points with integer coordinates on a UxU grid. The goal is to support reporting all k points inside an axis-aligned query rectangle. This is one of the most fundamental data structure problems in databases and computational geometry. Despite the importance of the problem its complexity remains unresolved in the word-RAM.

On the upper bound side, three best tradeoffs exist, all derived by reducing range reporting to a ball-inheritance problem. Ball-inheritance is a problem that essentially encapsulates all previous attempts at solving range reporting in the word-RAM. In this paper we make progress towards closing the gap between the upper and lower bounds for range reporting by proving cell probe lower bounds for ball-inheritance. Our lower bounds are tight for a large range of parameters, excluding any further progress for range reporting using the ball-inheritance reduction.

BibTeX - Entry

@InProceedings{grnlund_et_al:LIPIcs:2016:6193,
  author =	{Allan Gr\onlund and Kasper Green Larsen},
  title =	{{Towards Tight Lower Bounds for Range Reporting on the RAM}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{92:1--92:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6193},
  URN =		{urn:nbn:de:0030-drops-61936},
  doi =		{10.4230/LIPIcs.ICALP.2016.92},
  annote =	{Keywords: Data Structures, Lower Bounds, Cell Probe Model, Range Reporting}
}

Keywords: Data Structures, Lower Bounds, Cell Probe Model, Range Reporting
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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