4 Search Results for "Alzamel, Mai"

Document
DOI: 10.4230/LIPIcs.CPM.2021.5
The k-Mappability Problem Revisited

Authors: Amihood Amir, Itai Boneh, and Eitan Kondratovsky

Published in: LIPIcs, Volume 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)

Abstract
The k-mappability problem has two integers parameters m and k. For every subword of size m in a text S, we wish to report the number of indices in S in which the word occurs with at most k mismatches. The problem was lately tackled by Alzamel et al. [Mai Alzamel et al., 2018]. For a text with constant alphabet Σ and k ∈ O(1), they present an algorithm with linear space and O(nlog^{k+1}n) time. For the case in which k = 1 and a constant size alphabet, a faster algorithm with linear space and O(nlog(n)log log(n)) time was presented in [Mai Alzamel et al., 2020]. In this work, we enhance the techniques of [Mai Alzamel et al., 2020] to obtain an algorithm with linear space and O(n log(n)) time for k = 1. Our algorithm removes the constraint of the alphabet being of constant size. We also present linear algorithms for the case of k = 1, |Σ| ∈ O(1) and m = Ω(√n).
Cite as

Amihood Amir, Itai Boneh, and Eitan Kondratovsky. The k-Mappability Problem Revisited. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{amir_et_al:LIPIcs.CPM.2021.5,
  author =	{Amir, Amihood and Boneh, Itai and Kondratovsky, Eitan},
  title =	{{The k-Mappability Problem Revisited}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.5},
  URN =		{urn:nbn:de:0030-drops-139566},
  doi =		{10.4230/LIPIcs.CPM.2021.5},
  annote =	{Keywords: Pattern Matching, Hamming Distance, Suffix Tree, Suffix Array}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.2
Finding the Anticover of a String

Authors: Mai Alzamel, Alessio Conte, Shuhei Denzumi, Roberto Grossi, Costas S. Iliopoulos, Kazuhiro Kurita, and Kunihiro Wasa

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

Abstract
A k-anticover of a string x is a set of pairwise distinct factors of x of equal length k, such that every symbol of x is contained into an occurrence of at least one of those factors. The existence of a k-anticover can be seen as a notion of non-redundancy, which has application in computational biology, where they are associated with various non-regulatory mechanisms. In this paper we address the complexity of the problem of finding a k-anticover of a string x if it exists, showing that the decision problem is NP-complete on general strings for k ≥ 3. We also show that the problem admits a polynomial-time solution for k=2. For unbounded k, we provide an exact exponential algorithm to find a k-anticover of a string of length n (or determine that none exists), which runs in O*(min {3^{(n-k)/3)}, ((k(k+1))/2)^{n/(k+1)) time using polynomial space.
Cite as

Mai Alzamel, Alessio Conte, Shuhei Denzumi, Roberto Grossi, Costas S. Iliopoulos, Kazuhiro Kurita, and Kunihiro Wasa. Finding the Anticover of a String. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 2:1-2:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alzamel_et_al:LIPIcs.CPM.2020.2,
  author =	{Alzamel, Mai and Conte, Alessio and Denzumi, Shuhei and Grossi, Roberto and Iliopoulos, Costas S. and Kurita, Kazuhiro and Wasa, Kunihiro},
  title =	{{Finding the Anticover of a String}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{2:1--2:11},
  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.2020.2},
  URN =		{urn:nbn:de:0030-drops-121270},
  doi =		{10.4230/LIPIcs.CPM.2020.2},
  annote =	{Keywords: Anticover, String algorithms, Stringology, NP-complete}
}
Document
DOI: 10.4230/LIPIcs.CPM.2019.25
Quasi-Linear-Time Algorithm for Longest Common Circular Factor

Authors: Mai Alzamel, Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, and Wiktor Zuba

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)

Abstract
We introduce the Longest Common Circular Factor (LCCF) problem in which, given strings S and T of length at most n, we are to compute the longest factor of S whose cyclic shift occurs as a factor of T. It is a new similarity measure, an extension of the classic Longest Common Factor. We show how to solve the LCCF problem in O(n log^4 n) time using O(n log^2 n) space.
Cite as

Mai Alzamel, Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, and Wiktor Zuba. Quasi-Linear-Time Algorithm for Longest Common Circular Factor. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{alzamel_et_al:LIPIcs.CPM.2019.25,
  author =	{Alzamel, Mai and Crochemore, Maxime and Iliopoulos, Costas S. and Kociumaka, Tomasz and Radoszewski, Jakub and Rytter, Wojciech and Straszy\'{n}ski, Juliusz and Wale\'{n}, Tomasz and Zuba, Wiktor},
  title =	{{Quasi-Linear-Time Algorithm for Longest Common Circular Factor}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.25},
  URN =		{urn:nbn:de:0030-drops-104961},
  doi =		{10.4230/LIPIcs.CPM.2019.25},
  annote =	{Keywords: longest common factor, circular pattern matching, internal pattern matching, intersection of hyperrectangles}
}
Document
DOI: 10.4230/LIPIcs.WABI.2018.21
Degenerate String Comparison and Applications

Authors: Mai Alzamel, Lorraine A. K. Ayad, Giulia Bernardini, Roberto Grossi, Costas S. Iliopoulos, Nadia Pisanti, Solon P. Pissis, and Giovanna Rosone

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
A generalised degenerate string (GD string) S^ is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length k_i but this length can vary between different sets. We denote the sum of these lengths k_0, k_1,...,k_{n-1} by W. This type of uncertain sequence can represent, for example, a gapless multiple sequence alignment of width W in a compact form. Our first result in this paper is an O(N+M)-time algorithm for deciding whether the intersection of two GD strings of total sizes N and M, respectively, over an integer alphabet, is non-empty. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in only linear space. A similar result can be obtained by employing an automata-based approach but its cost is alphabet-dependent. We then apply our string comparison algorithm to compute palindromes in GD strings. We present an O(min{W,n^2}N)-time algorithm for computing all palindromes in S^. Furthermore, we show a similar conditional lower bound for computing maximal palindromes in S^. Finally, proof-of-concept experimental results are presented using real protein datasets.
Cite as

Mai Alzamel, Lorraine A. K. Ayad, Giulia Bernardini, Roberto Grossi, Costas S. Iliopoulos, Nadia Pisanti, Solon P. Pissis, and Giovanna Rosone. Degenerate String Comparison and Applications. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{alzamel_et_al:LIPIcs.WABI.2018.21,
  author =	{Alzamel, Mai and Ayad, Lorraine A. K. and Bernardini, Giulia and Grossi, Roberto and Iliopoulos, Costas S. and Pisanti, Nadia and Pissis, Solon P. and Rosone, Giovanna},
  title =	{{Degenerate String Comparison and Applications}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.21},
  URN =		{urn:nbn:de:0030-drops-93236},
  doi =		{10.4230/LIPIcs.WABI.2018.21},
  annote =	{Keywords: degenerate strings, generalised degenerate strings, elastic-degenerate strings, string comparison, palindromes}
}
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