License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
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DOI: 10.4230/LIPIcs.STACS.2012.112
URN: urn:nbn:de:0030-drops-34101
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3410/
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Stølting Brodal, Gerth ; Kejlberg-Rasmussen, Casper

Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property

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Abstract

In this paper we present an implicit dynamic dictionary with the working-set property, supporting insert(e) and delete(e) in O(log n) time, predecessor(e) in O(log l_{p(e)}) time, successor(e) in O(log l_{s(e)}) time and search(e) in O(log min(l_{p(e)},l_{e}, l_{s(e)})) time, where n is the number of elements stored in the dictionary, l_{e} is the number of distinct elements searched for since element e was last searched for and p(e) and s(e) are the predecessor and successor of e, respectively. The time-bounds are all worst-case. The dictionary stores the elements in an array of size n using *no* additional space. In the cache-oblivious model the log is base B and the cache-obliviousness is due to our black box use of an existing cache-oblivious implicit dictionary. This is the first implicit dictionary supporting predecessor and successor searches in the working-set bound. Previous implicit structures required O(log n) time.

BibTeX - Entry

@InProceedings{stltingbrodal_et_al:LIPIcs:2012:3410,
  author =	{Gerth St\olting Brodal and Casper Kejlberg-Rasmussen},
  title =	{{Cache-Oblivious Implicit Predecessor Dictionaries with the Working-Set Property}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{112--123},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{Christoph D{\"u}rr and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3410},
  URN =		{urn:nbn:de:0030-drops-34101},
  doi =		{10.4230/LIPIcs.STACS.2012.112},
  annote =	{Keywords: working-set property, dictionary, implicit, cache-oblivious, worst-case, external memory, I/O efficient}
}

Keywords: working-set property, dictionary, implicit, cache-oblivious, worst-case, external memory, I/O efficient
Collection: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue Date: 2012
Date of publication: 24.02.2012

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