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.FSTTCS.2016.35
URN: urn:nbn:de:0030-drops-68700
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6870/
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Gawrychowski, Pawel ; Jez, Artur

LZ77 Factorisation of Trees

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LIPIcs-FSTTCS-2016-35.pdf (0.5 MB)

Abstract

We generalise the fundamental concept of LZ77 factorisation from strings to trees. A tree is represented as a collection of edge-disjoint fragments that either consist of one node or has already occurred earlier (in the BFS order). Similarly as for strings, such a collection uniquely determines the tree, so by minimising the number of fragments we obtain a compressed representation of the tree. We show that our generalisation has several useful properties of the standard LZ77 factorisation: it can be computed in polynomial time and its simpler variant in linear time; its size is not larger than the smallest grammar for a tree; it can be transformed (in linear time) into a tree grammar of size O(rg log(n/(rg))), where n is the size of the tree, g the size of the smallest grammar for this tree and r the maximal arity of the nodes in the tree, which matches a recent bound of Jez and Lohrey [STACS 2014], but with a simpler and more modular proof.

BibTeX - Entry

@InProceedings{gawrychowski_et_al:LIPIcs:2016:6870,
  author =	{Pawel Gawrychowski and Artur Jez},
  title =	{{LZ77 Factorisation of Trees}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Akash Lal and S. Akshay and Saket Saurabh and Sandeep Sen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6870},
  URN =		{urn:nbn:de:0030-drops-68700},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.35},
  annote =	{Keywords: Tree grammars, Grammar compression, LZ77, SLP, Tree compression}
}

Keywords: Tree grammars, Grammar compression, LZ77, SLP, Tree compression
Collection: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)
Issue Date: 2016
Date of publication: 10.12.2016

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