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Finding Maximal 2-Dimensional Palindromes

Authors: Sara Geizhals and Dina Sokol

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)


Abstract
This paper extends the problem of palindrome searching into a higher dimension, addressing two definitions of 2D palindromes. The first definition implies a square, while the second definition (also known as a centrosymmetric factor), can be any rectangular shape. We describe two algorithms for searching a 2D text for maximal palindromes, one for each type of 2D palindrome. The first algorithm is optimal; it runs in linear time, on par with Manacher's linear time 1D palindrome algorithm. The second algorithm searches a text of size n_1 x n_2 (n_1 >= n_2) in O(n_2) time for each of its n_1 x n_2 positions. Since each position may have up to O(n_2) maximal palindromes centered at that location, the second result is also optimal in terms of the worst-case output size.

Cite as

Sara Geizhals and Dina Sokol. Finding Maximal 2-Dimensional Palindromes. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{geizhals_et_al:LIPIcs.CPM.2016.19,
  author =	{Geizhals, Sara and Sokol, Dina},
  title =	{{Finding Maximal 2-Dimensional Palindromes}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{19:1--19:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.19},
  URN =		{urn:nbn:de:0030-drops-60752},
  doi =		{10.4230/LIPIcs.CPM.2016.19},
  annote =	{Keywords: palindrome, pattern matching, 2-Dimensional, centrosymmetric factor}
}
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