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.FSTTCS.2017.20
URN: urn:nbn:de:0030-drops-83892
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8389/
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Boninger, Joseph ; Brody, Joshua ; Kephart, Owen

Non-Adaptive Data Structure Bounds for Dynamic Predecessor

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LIPIcs-FSTTCS-2017-20.pdf (0.5 MB)

Abstract

In this work, we continue the examination of the role non-adaptivity plays in maintaining dynamic data structures, initiated by Brody and Larsen. We consider non-adaptive data structures for predecessor search in the w-bit cell probe model. In this problem, the goal is to dynamically maintain a subset T of up to n elements from
{1, ..., m}, while supporting insertions, deletions, and a predecessor query Pred(x), which returns the largest element in T that is less than or equal to x. Predecessor search is one of the most well-studied data structure problems. For this problem, using non-adaptivity comes at a steep price. We provide exponential cell probe complexity separations between (i) adaptive and non-adaptive data structures and (ii) non-adaptive and memoryless data structures for predecessor search.

A classic data structure of van Emde Boas solves dynamic predecessor search in log(log(m)) probes; this data structure is adaptive. For dynamic data structures which make non-adaptive updates, we show the cell probe complexity is O(log(m)/log(w/log(m))). We also give a nearly-matching Omega(log(m)/log(w)) lower bound. We also give an m/w lower bound for memoryless data structures.

Our lower bound technique is tailored to non-adaptive (as opposed to memoryless) updates and might be of independent interest.

BibTeX - Entry

@InProceedings{boninger_et_al:LIPIcs:2018:8389,
  author =	{Joseph Boninger and Joshua Brody and Owen Kephart},
  title =	{{Non-Adaptive Data Structure Bounds for Dynamic Predecessor}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{20:1--20:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8389},
  URN =		{urn:nbn:de:0030-drops-83892},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.20},
  annote =	{Keywords: dynamic data structures, lower bounds, predecessor search, non-adaptivity}
}

Keywords: dynamic data structures, lower bounds, predecessor search, non-adaptivity
Collection: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 12.02.2018

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