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.STACS.2018.22
URN: urn:nbn:de:0030-drops-85088
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8508/
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Clifford, Raphaël ; Grønlund, Allan ; Larsen, Kasper Green ; Starikovskaya, Tatiana

Upper and Lower Bounds for Dynamic Data Structures on Strings

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LIPIcs-STACS-2018-22.pdf (0.5 MB)

Abstract

We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length m and a substring of a longer text. We give both conditional and unconditional lower bounds for variants of exact matching with wildcards, inner product, and Hamming distance computation via a sequence of reductions. As an example, we show that there does not exist an O(m^{1/2-epsilon}) time algorithm for a large range of these problems unless the online Boolean matrix-vector multiplication conjecture is false. We also provide nearly matching upper bounds for most of the problems we consider.

BibTeX - Entry

@InProceedings{clifford_et_al:LIPIcs:2018:8508,
  author =	{Rapha{\"e}l Clifford and Allan Gr\onlund and Kasper Green Larsen and Tatiana Starikovskaya},
  title =	{{Upper and Lower Bounds for Dynamic Data Structures on Strings}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8508},
  URN =		{urn:nbn:de:0030-drops-85088},
  doi =		{10.4230/LIPIcs.STACS.2018.22},
  annote =	{Keywords: exact pattern matching with wildcards, hamming distance, inner product, conditional lower bounds}
}

Keywords: exact pattern matching with wildcards, hamming distance, inner product, conditional lower bounds
Collection: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 27.02.2018

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