License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2022.23
URN: urn:nbn:de:0030-drops-161508
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Radoszewski, Jakub ; Rytter, Wojciech ; Straszyński, Juliusz ; Waleń, Tomasz ; Zuba, Wiktor

Rectangular Tile Covers of 2D-Strings

LIPIcs-CPM-2022-23.pdf (0.7 MB)


We consider tile covers of 2D-strings which are a generalization of periodicity of 1D-strings. We say that a 2D-string A is a tile cover of a 2D-string S if S can be decomposed into non-overlapping 2D-strings, each of them equal to A or to A^T, where A^T is the transpose of A. We show that all tile covers of a 2D-string of size N can be computed in ?(N^{1+ε}) time for any ε > 0. We also show a linear-time algorithm for computing all 1D-strings being tile covers of a 2D-string.

BibTeX - Entry

  author =	{Radoszewski, Jakub and Rytter, Wojciech and Straszy\'{n}ski, Juliusz and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Rectangular Tile Covers of 2D-Strings}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-161508},
  doi =		{10.4230/LIPIcs.CPM.2022.23},
  annote =	{Keywords: tile cover, periodicity, efficient algorithm}

Keywords: tile cover, periodicity, efficient algorithm
Collection: 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)
Issue Date: 2022
Date of publication: 22.06.2022

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