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.2019.4
URN: urn:nbn:de:0030-drops-115000
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11500/
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Bille, Philip ; Gawrychowski, Pawel ; Gørtz, Inge Li ; Landau, Gad M. ; Weimann, Oren

Top Tree Compression of Tries

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LIPIcs-ISAAC-2019-4.pdf (5 MB)

Abstract

We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to preprocess a set of strings of total length n over an alphabet of size sigma into a compressed data structure of worst-case optimal size O(n/log_sigma n) that given a pattern string P of length m determines if P is a prefix of one of the strings in time O(min(m log sigma,m + log n)). We show that this query time is in fact optimal regardless of the size of the data structure.
Existing solutions either use Omega(n) space or rely on word RAM techniques, such as tabulation, hashing, address arithmetic, or word-level parallelism, and hence do not work on a pointer machine. Our result is the first solution on a pointer machine that achieves worst-case o(n) space. Along the way, we develop several interesting data structures that work on a pointer machine and are of independent interest. These include an optimal data structures for random access to a grammar-compressed string and an optimal data structure for a variant of the level ancestor problem.

BibTeX - Entry

@InProceedings{bille_et_al:LIPIcs:2019:11500,
  author =	{Philip Bille and Pawel Gawrychowski and Inge Li G{\o}rtz and Gad M. Landau and Oren Weimann},
  title =	{{Top Tree Compression of Tries}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11500},
  URN =		{urn:nbn:de:0030-drops-115000},
  doi =		{10.4230/LIPIcs.ISAAC.2019.4},
  annote =	{Keywords: pattern matching, tree compression, top trees, pointer machine}
}

Keywords: pattern matching, tree compression, top trees, pointer machine
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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