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Documents authored by Miclăuş, Adrian

Document
DOI: 10.4230/LIPIcs.CPM.2024.10
Searching 2D-Strings for Matching Frames

Authors: Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Miclăuş, and Arseny Shur

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
We study a natural type of repetitions in 2-dimensional strings. Such a repetition, called a matching frame, is a rectangular substring of size at least 2× 2 with equal marginal rows and equal marginal columns. Matching frames first appeared in literature in the context of Wang tiles. We present two algorithms finding a matching frame with the maximum perimeter in a given n× m input string. The first algorithm solves the problem exactly in Õ(n^{2.5}) time (assuming n ≥ m). The second algorithm finds a (1-ε)-approximate solution in Õ((nm)/ε⁴) time, which is near linear in the size of the input for constant ε. In particular, by setting ε = O(1) the second algorithm decides the existence of a matching frame in a given string in Õ(nm) time. Some technical elements and structural properties used in these algorithms can be of independent interest.
Cite as

Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Miclăuş, and Arseny Shur. Searching 2D-Strings for Matching Frames. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2024.10,
  author =	{Boneh, Itai and Fried, Dvir and Golan, Shay and Kraus, Matan and Micl\u{a}u\c{s}, Adrian and Shur, Arseny},
  title =	{{Searching 2D-Strings for Matching Frames}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.10},
  URN =		{urn:nbn:de:0030-drops-201205},
  doi =		{10.4230/LIPIcs.CPM.2024.10},
  annote =	{Keywords: 2D string, matching frame, LCP, multidimensional range query}
}
Document
DOI: 10.4230/LIPIcs.CPM.2023.5
Faster Algorithms for Computing the Hairpin Completion Distance and Minimum Ancestor

Authors: Itai Boneh, Dvir Fried, Adrian Miclăuş, and Alexandru Popa

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

Abstract
Hairpin completion is an operation on formal languages that has been inspired by hairpin formation in DNA biochemistry and has many applications especially in DNA computing. Consider s to be a string over the alphabet {A, C, G, T} such that a prefix/suffix of it matches the reversed complement of a substring of s. Then, in a hairpin completion operation the reversed complement of this prefix/suffix is added to the start/end of s forming a new string. In this paper we study two problems related to the hairpin completion. The first problem asks the minimum number of hairpin operations necessary to transform one string into another, number that is called the hairpin completion distance. For this problem we show an algorithm of running time O(n²), where n is the maximum length of the two strings. Our algorithm improves on the algorithm of Manea (TCS 2010), that has running time O(n² log n). In the minimum distance common hairpin completion ancestor problem we want to find, for two input strings x and y, a string w that minimizes the sum of the hairpin completion distances to x and y. Similarly, we present an algorithm with running time O(n²) that improves by a O(log n) factor the algorithm of Manea (TCS 2010).
Cite as

Itai Boneh, Dvir Fried, Adrian Miclăuş, and Alexandru Popa. Faster Algorithms for Computing the Hairpin Completion Distance and Minimum Ancestor. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2023.5,
  author =	{Boneh, Itai and Fried, Dvir and Micl\u{a}u\c{s}, Adrian and Popa, Alexandru},
  title =	{{Faster Algorithms for Computing the Hairpin Completion Distance and Minimum Ancestor}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{5:1--5:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.5},
  URN =		{urn:nbn:de:0030-drops-179592},
  doi =		{10.4230/LIPIcs.CPM.2023.5},
  annote =	{Keywords: dynamic programming, incremental trees, exact algorithm}
}
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