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Documents authored by Badkobeh, Golnaz

Document
DOI: 10.4230/LIPIcs.CPM.2022.13
Back-To-Front Online Lyndon Forest Construction

Authors: Golnaz Badkobeh, Maxime Crochemore, Jonas Ellert, and Cyril Nicaud

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
A Lyndon word is a word that is lexicographically smaller than all of its non-trivial rotations (e.g. ananas is a Lyndon word; banana is not a Lyndon word due to its smaller rotation abanan). The Lyndon forest (or equivalently Lyndon table) identifies maximal Lyndon factors of a word, and is of great combinatoric interest, e.g. when finding maximal repetitions in words. While optimal linear time algorithms for computing the Lyndon forest are known, none of them work in an online manner. We present algorithms that compute the Lyndon forest of a word in a reverse online manner, processing the input word from back to front. We assume a general ordered alphabet, i.e. the only elementary operations on symbols are comparisons of the form less-equal-greater. We start with a naive algorithm and show that, despite its quadratic worst-case behaviour, it already takes expected linear time on words drawn uniformly at random. We then introduce a much more sophisticated algorithm that takes linear time in the worst case. It borrows some ideas from the offline algorithm by Bille et al. (ICALP 2020), combined with new techniques that are necessary for the reverse online setting. While the back-to-front approach for this computation is rather natural (see Franek and Liut, PSC 2019), the steps required to achieve linear time are surprisingly intricate. We envision that our algorithm will be useful for the online computation of maximal repetitions in words.
Cite as

Golnaz Badkobeh, Maxime Crochemore, Jonas Ellert, and Cyril Nicaud. Back-To-Front Online Lyndon Forest Construction. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{badkobeh_et_al:LIPIcs.CPM.2022.13,
  author =	{Badkobeh, Golnaz and Crochemore, Maxime and Ellert, Jonas and Nicaud, Cyril},
  title =	{{Back-To-Front Online Lyndon Forest Construction}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{13:1--13:23},
  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 =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.13},
  URN =		{urn:nbn:de:0030-drops-161404},
  doi =		{10.4230/LIPIcs.CPM.2022.13},
  annote =	{Keywords: Lyndon factorisation, Lyndon forest, Lyndon table, Lyndon array, right Lyndon tree, Cartesian tree, standard factorisation, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.CPM.2021.6
Internal Shortest Absent Word Queries

Authors: Golnaz Badkobeh, Panagiotis Charalampopoulos, and Solon P. Pissis

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

Abstract
Given a string T of length n over an alphabet Σ ⊂ {1,2,…,n^{𝒪(1)}} of size σ, we are to preprocess T so that given a range [i,j], we can return a representation of a shortest string over Σ that is absent in the fragment T[i]⋯ T[j] of T. For any positive integer k ∈ [1,log log_σ n], we present an 𝒪((n/k)⋅ log log_σ n)-size data structure, which can be constructed in 𝒪(nlog_σ n) time, and answers queries in time 𝒪(log log_σ k).
Cite as

Golnaz Badkobeh, Panagiotis Charalampopoulos, and Solon P. Pissis. Internal Shortest Absent Word Queries. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{badkobeh_et_al:LIPIcs.CPM.2021.6,
  author =	{Badkobeh, Golnaz and Charalampopoulos, Panagiotis and Pissis, Solon P.},
  title =	{{Internal Shortest Absent Word Queries}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{6:1--6:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.6},
  URN =		{urn:nbn:de:0030-drops-139570},
  doi =		{10.4230/LIPIcs.CPM.2021.6},
  annote =	{Keywords: string algorithms, internal queries, shortest absent word, bit parallelism}
}
Document
DOI: 10.4230/LIPIcs.CPM.2019.32
Computing the Antiperiod(s) of a String

Authors: Hayam Alamro, Golnaz Badkobeh, Djamal Belazzougui, Costas S. Iliopoulos, and Simon J. Puglisi

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

Abstract
A string S[1,n] is a power (or repetition or tandem repeat) of order k and period n/k, if it can be decomposed into k consecutive identical blocks of length n/k. Powers and periods are fundamental structures in the study of strings and algorithms to compute them efficiently have been widely studied. Recently, Fici et al. (Proc. ICALP 2016) introduced an antipower of order k to be a string composed of k distinct blocks of the same length, n/k, called the antiperiod. An arbitrary string will have antiperiod t if it is prefix of an antipower with antiperiod t. In this paper, we describe efficient algorithm for computing the smallest antiperiod of a string S of length n in O(n) time. We also describe an algorithm to compute all the antiperiods of S that runs in O(n log n) time.
Cite as

Hayam Alamro, Golnaz Badkobeh, Djamal Belazzougui, Costas S. Iliopoulos, and Simon J. Puglisi. Computing the Antiperiod(s) of a String. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 32:1-32:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{alamro_et_al:LIPIcs.CPM.2019.32,
  author =	{Alamro, Hayam and Badkobeh, Golnaz and Belazzougui, Djamal and Iliopoulos, Costas S. and Puglisi, Simon J.},
  title =	{{Computing the Antiperiod(s) of a String}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{32:1--32:11},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.32},
  URN =		{urn:nbn:de:0030-drops-105035},
  doi =		{10.4230/LIPIcs.CPM.2019.32},
  annote =	{Keywords: antiperiod, antipower, power, period, repetition, run, string}
}
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