Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Dvořák, Pavel; Loff, Bruno https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-132617
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Lower Bounds for Semi-adaptive Data Structures via Corruption

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Abstract

In a dynamic data structure problem we wish to maintain an encoding of some data in memory, in such a way that we may efficiently carry out a sequence of queries and updates to the data. A long-standing open problem in this area is to prove an unconditional polynomial lower bound of a trade-off between the update time and the query time of an adaptive dynamic data structure computing some explicit function. Ko and Weinstein provided such lower bound for a restricted class of semi-adaptive data structures, which compute the Disjointness function. There, the data are subsets x₁,… ,x_k and y of {1,… ,n}, the updates can modify y (by inserting and removing elements), and the queries are an index i ∈ {1,… ,k} (query i should answer whether x_i and y are disjoint, i.e., it should compute the Disjointness function applied to (x_i, y)). The semi-adaptiveness places a restriction in how the data structure can be accessed in order to answer a query. We generalize the lower bound of Ko and Weinstein to work not just for the Disjointness, but for any function having high complexity under the smooth corruption bound.

BibTeX - Entry

@InProceedings{dvok_et_al:LIPIcs:2020:13261,
  author =	{Pavel Dvoř{\'a}k and Bruno Loff},
  title =	{{Lower Bounds for Semi-adaptive Data Structures via Corruption}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Nitin Saxena and Sunil Simon},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13261},
  URN =		{urn:nbn:de:0030-drops-132617},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.20},
  annote =	{Keywords: semi-adaptive dynamic data structure, polynomial lower bound, corruption bound, information theory}
}

Keywords: semi-adaptive dynamic data structure, polynomial lower bound, corruption bound, information theory
Seminar: 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)
Issue date: 2020
Date of publication: 04.12.2020


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