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.ISAAC.2017.44
URN: urn:nbn:de:0030-drops-82527
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8252/
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Hagerup, Torben ; Kammer, Frank

On-the-Fly Array Initialization in Less Space

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LIPIcs-ISAAC-2017-44.pdf (0.5 MB)

Abstract

We show that for all given n,t,w in {1,2,...} with n<2^w, an array of n entries of w bits each can be represented on a word RAM with a word length of w bits in at most nw+ceil(n(t/(2 w))^t) bits of uninitialized memory to support constant-time initialization of the whole array and O(t)-time reading and writing of individual array entries. At one end of this tradeoff, we achieve initialization and access (i.e., reading and writing) in constant time with nw+ceil(n/w^t) bits for arbitrary fixed t, to be compared with nw+Theta(n) bits for the best previous solution, and at the opposite end, still with constant-time initialization, we support O(log n)-time access with just nw+1 bits, which is optimal for arbitrary access times if the initialization executes fewer than n steps.

BibTeX - Entry

@InProceedings{hagerup_et_al:LIPIcs:2017:8252,
  author =	{Torben Hagerup and Frank Kammer},
  title =	{{On-the-Fly Array Initialization in Less Space}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{44:1--44:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8252},
  URN =		{urn:nbn:de:0030-drops-82527},
  doi =		{10.4230/LIPIcs.ISAAC.2017.44},
  annote =	{Keywords: data structures, space efficiency, constant-time initialization, on-the-fly initialization, arrays}
}

Keywords: data structures, space efficiency, constant-time initialization, on-the-fly initialization, arrays
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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