2 Search Results for "Ghazawi, Samah"

Document
DOI: 10.4230/LIPIcs.CPM.2023.13
Order-Preserving Squares in Strings

Authors: Paweł Gawrychowski, Samah Ghazawi, and Gad M. Landau

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract
An order-preserving square in a string is a fragment of the form uv where u ≠ v and u is order-isomorphic to v. We show that a string w of length n over an alphabet of size σ contains 𝒪(σn) order-preserving squares that are distinct as words. This improves the upper bound of 𝒪(σ²n) by Kociumaka, Radoszewski, Rytter, and Waleń [TCS 2016]. Further, for every σ and n we exhibit a string with Ω(σn) order-preserving squares that are distinct as words, thus establishing that our upper bound is asymptotically tight. Finally, we design an 𝒪(σn) time algorithm that outputs all order-preserving squares that occur in a given string and are distinct as words. By our lower bound, this is optimal in the worst case.
Cite as

Paweł Gawrychowski, Samah Ghazawi, and Gad M. Landau. Order-Preserving Squares in Strings. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2023.13,
  author =	{Gawrychowski, Pawe{\l} and Ghazawi, Samah and Landau, Gad M.},
  title =	{{Order-Preserving Squares in Strings}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.13},
  URN =		{urn:nbn:de:0030-drops-179676},
  doi =		{10.4230/LIPIcs.CPM.2023.13},
  annote =	{Keywords: repetitions, distinct squares, order-isomorphism}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.14
On Indeterminate Strings Matching

Authors: Paweł Gawrychowski, Samah Ghazawi, and Gad M. Landau

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
Given two indeterminate equal-length strings p and t with a set of characters per position in both strings, we obtain a determinate string p_w from p and a determinate string t_w from t by choosing one character per position. Then, we say that p and t match when p_w and t_w match for some choice of the characters. While the most standard notion of a match for determinate strings is that they are simply identical, in certain applications it is more appropriate to use other definitions, with the prime examples being parameterized matching, order-preserving matching, and the recently introduced Cartesian tree matching. We provide a systematic study of the complexity of string matching for indeterminate equal-length strings, for different notions of matching. We use n to denote the length of both strings, and r to be an upper-bound on the number of uncertain characters per position. First, we provide the first polynomial time algorithm for the Cartesian tree version that runs in deterministic 𝒪(nlog² n) and expected 𝒪(nlog nlog log n) time using 𝒪(nlog n) space, for constant r. Second, we establish NP-hardness of the order-preserving version for r=2, thus solving a question explicitly stated by Henriques et al. [CPM 2018], who showed hardness for r=3. Third, we establish NP-hardness of the parameterized version for r=2. As both parameterized and order-preserving indeterminate matching reduce to the standard determinate matching for r=1, this provides a complete classification for these three variants.
Cite as

Paweł Gawrychowski, Samah Ghazawi, and Gad M. Landau. On Indeterminate Strings Matching. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2020.14,
  author =	{Gawrychowski, Pawe{\l} and Ghazawi, Samah and Landau, Gad M.},
  title =	{{On Indeterminate Strings Matching}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.14},
  URN =		{urn:nbn:de:0030-drops-121393},
  doi =		{10.4230/LIPIcs.CPM.2020.14},
  annote =	{Keywords: string matching, indeterminate strings, Cartesian trees, order-preserving matching, parameterized matching}
}
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