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.CPM.2018.16
URN: urn:nbn:de:0030-drops-86920
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Dudek, Bartlomiej ; Gawrychowski, Pawel

Slowing Down Top Trees for Better Worst-Case Compression

LIPIcs-CPM-2018-16.pdf (0.5 MB)


We consider the top tree compression scheme introduced by Bille et al. [ICALP 2013] and construct an infinite family of trees on n nodes labeled from an alphabet of size sigma, for which the size of the top DAG is Theta(n/log_sigma n log log_sigma n). Our construction matches a previously known upper bound and exhibits a weakness of this scheme, as the information-theoretic lower bound is Omega(n/log_sigma n}). This settles an open problem stated by Lohrey et al. [arXiv 2017], who designed a more involved version achieving the lower bound. We show that this can be also guaranteed by a very minor modification of the original scheme: informally, one only needs to ensure that different parts of the tree are not compressed too quickly. Arguably, our version is more uniform, and in particular, the compression procedure is oblivious to the value of sigma.

BibTeX - Entry

  author =	{Bartlomiej Dudek and Pawel Gawrychowski},
  title =	{{Slowing Down Top Trees for Better Worst-Case Compression}},
  booktitle =	{Annual Symposium on Combinatorial Pattern Matching  (CPM 2018)},
  pages =	{16:1--16:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Gonzalo Navarro and David Sankoff and Binhai Zhu},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-86920},
  doi =		{10.4230/LIPIcs.CPM.2018.16},
  annote =	{Keywords: top trees, compression, tree grammars}

Keywords: top trees, compression, tree grammars
Collection: Annual Symposium on Combinatorial Pattern Matching (CPM 2018)
Issue Date: 2018
Date of publication: 18.05.2018

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