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LZ77 Factorisation of Trees

Authors Pawel Gawrychowski, Artur Jez

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Pawel Gawrychowski
Artur Jez

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Pawel Gawrychowski and Artur Jez. LZ77 Factorisation of Trees. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.FSTTCS.2016.35

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.
Keywords
  • Tree grammars
  • Grammar compression
  • LZ77
  • SLP
  • Tree compression

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