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Space Efficient Construction of Lyndon Arrays in Linear Time [article]

Philip Bille, Jonas Ellert, Johannes Fischer, Inge Li Gørtz, Florian Kurpicz, Ian Munro, Eva Rotenberg
2019 arXiv   pre-print
We present the first linear time algorithm to construct the 2n-bit version of the Lyndon array for a string of length n using only o(n) bits of working space.  ...  Also in practice, our new algorithms outperform the previous best ones by an order of magnitude, both in terms of time and space.  ...  The construction algorithm can also produce the (non-succinct) Lyndon array in linear time using only O(1) words of working space.  ... 
arXiv:1911.03542v2 fatcat:nygmqmb2dncr7nvnpzfrncmuoa

Space Efficient Construction of Lyndon Arrays in Linear Time

Philip Bille, Jonas Ellert, Johannes Fischer, Inge Li Gørtz, Florian Kurpicz, J. Ian Munro, Eva Rotenberg, Emanuela Merelli, Artur Czumaj, Anuj Dawar
2020 International Colloquium on Automata, Languages and Programming  
We show that, in fact, o(n) additional bits are sufficient to compute the succinct 2n-bit version of the Lyndon array in linear time.  ...  Our space efficient construction algorithm makes the Lyndon array more accessible as a fundamental data structure in applications like full-text indexing.  ...  We have shown: 14:16 Space Efficient Construction of Lyndon Arrays in Linear Time The algorithm can easily be adapted to compute the Lyndon array instead of the PSS tree.  ... 
doi:10.4230/lipics.icalp.2020.14 dblp:conf/icalp/BilleE0GKMR20 fatcat:vovgnfe4bzdjneygn36ukpj47i

Linear Algorithms for Computing the Lyndon Border Array and the Lyndon Suffix Array [article]

Ali Alatabbi, Jacqueline W. Daykin, M. Sohel Rahman
2015 arXiv   pre-print
Further, we introduce the Lyndon Suffix Array, and by modifying the efficient suffix array technique of Ko and Aluru KA03 outline a linear time and space algorithm for its construction.  ...  We propose linear-time and linear-space algorithms for computing L β (s). binary and bounded alphabets.  ...  In order to efficiently construct the Lyndon suffix array we could directly modify the linear-time and space efficient method of Ko and Aluru [KA03] given for the original data structure -this would  ... 
arXiv:1506.06983v1 fatcat:ndguexynefe5tbtngdvojio4om

Extended suffix array construction using Lyndon factors

Sunita, Deepak Garg
2018 Sadhana (Bangalore)  
In this paper, we are extending the novel approach of incremental suffix array construction using Lyndon factorization to the construction of extended suffix array where extended suffix array is the suffix  ...  Incremental LCP construction simultaneously saves a lot of computation and hence time. The proposed approach has quadratic run time and the disk working space requirement is O(n).  ...  So, we can compute SA in linear time i.e., O(m) and O(m log m) bits of space using any of the existing linear time suffix array construction algorithm like libdivsufsort.  ... 
doi:10.1007/s12046-018-0832-z fatcat:nguhgupnpzh2dbfqdl2uqhvbfy

Inducing the Lyndon Array [article]

Felipe A. Louza, Sabrina Mantaci, Giovanni Manzini, Marinella Sciortino, Guilherme P. Telles
2019 arXiv   pre-print
Our result improves the previous best space requirement for linear time computation of the Lyndon array.  ...  In fact, all the known linear algorithms for Lyndon array computation use suffix sorting as a preprocessing step and use O(n) words of working space in addition to the Lyndon array and suffix array.  ...  Acknowledgments The authors thank Uwe Baier for kindly providing the source codes of algorithms Baier-LA and Baier-LA+SA, and Prof.  ... 
arXiv:1905.12987v2 fatcat:6mwhqkru3ncudhsnmvco7by2z4

Indeterminate String Factorizations and Degenerate Text Transformations

Jacqueline W. Daykin, Bruce Watson
2017 Mathematics in Computer Science  
Like the original forms, indeterminate Lyndon factorization and the degenerate transform and its inverse can all be computed in linear time and space with respect to total input size of degenerate strings  ...  For space efficiency the input to the transform can be preprocessed into Lyndon factors.  ...  For constructing the indeterminate suffix array we will apply a linear-time and space efficient method such as that of Ko and Aluru [22] given for the original data structure.  ... 
doi:10.1007/s11786-016-0285-x fatcat:dpic7m34xnctxlsraukgtngx6m

2D Lyndon Words and Applications [article]

Shoshana Marcus, Dina Sokol
2013 arXiv   pre-print
The final algorithm achieves linear time complexity even when the least common multiple of the periods of the rows is exponential in the matrix width.  ...  Lyndon words are used for constructing bases in free Lie algebras, constructing de Bruijn sequences, finding the lexicographically smallest or largest substring in a string, and succinct suffix-prefix  ...  In terms of space, the representative 2D Lyndon word is stored in O(m log m) bits since it is an array of m integers, each of which is between 0 and m/4.  ... 
arXiv:1301.0103v1 fatcat:gxb6t7y3rzcxff6cjrs2pwjppi

Sorting suffixes of a text via its Lyndon Factorization [article]

Sabrina Mantaci, Antonio Restivo, Giovanna Rosone, Marinella Sciortino
2013 arXiv   pre-print
They are used for instance in the constructions of the Burrows-Wheeler transform and the suffix array, widely used in several fields of Computer Science.  ...  The process of sorting the suffixes of a text plays a fundamental role in Text Algorithms.  ...  Duval in [11] presents two variants of an algorithm of factorization of a word into Lyndon words in time linear in the length of the word.  ... 
arXiv:1306.1366v1 fatcat:f657xqdlfzdctehp7ynp4m67dy

Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time [article]

Hideo Bannai and Juha Kärkkäinen and Dominik Köppl and Marcin Pia̧tkowski
2021 arXiv   pre-print
also be constructed in linear time.  ...  Although it is known that the BWT can be constructed in linear time for integer alphabets by using a linear time suffix array construction algorithm, it was up to now only conjectured that the BBWT can  ...  Let us start with the traditional BWT, which we can construct thanks to linear time suffix array construction algorithms [23, 17] [12] postulated that it can be built in linear time, but did not  ... 
arXiv:1911.06985v2 fatcat:bu7t7ukgvzfzdnfzuhoilfdul4

Minimal Suffix and Rotation of a Substring in Optimal Time

Tomasz Kociumaka, Marc Herbstritt
2016 Annual Symposium on Combinatorial Pattern Matching  
We develop a data structure answering such queries optimally: in constant time after linear-time preprocessing. This improves upon the results of Babenko et al.  ...  We apply these generalized queries to compute lexicographically minimal and maximal rotations of a given substring in constant time after linear-time preprocessing.  ...  Acknowledgements I would like to thank the remaining co-authors of [4] , collaboration with whom on earlier results about minimal and maximal suffixes sparked some of my ideas used in this paper.  ... 
doi:10.4230/lipics.cpm.2016.28 dblp:conf/cpm/Kociumaka16 fatcat:5ecfttqb4rcqraxd6ezwipepxq

Algorithms to Compute the Lyndon Array [article]

Frantisek Franek and A. S. M. Sohidull Islam and M. Sohel Rahman and W. F. Smyth
2016 arXiv   pre-print
Two of these algorithms execute in quadratic time in the worst case, the third achieves linear time, but at the expense of prior computation of both the suffix array and the inverse suffix array of x.  ...  We conjecture that there exists a fast and worst-case linear-time algorithm to compute the Lyndon array that is also elementary (making no use of global data structures such as the suffix array).  ...  This work was supported in part by the Natural Sciences & Engineering Research Council of Canada. The authors wish to thank Maxime Crochemore and Hideo Bannai for helpful discussions.  ... 
arXiv:1605.08935v1 fatcat:ae4wn4ijnjhj5h3t23ziynaxri

Small-Space 2D Compressed Dictionary Matching [chapter]

Shoshana Neuburger, Dina Sokol
2010 Lecture Notes in Computer Science  
The preprocessing time of the algorithm is O(km 2 ), linear in the uncompressed dictionary size, and the time for performing the search is linear in the uncompressed text size, independent of the dictionary  ...  ., the extra space it uses is proportional to the optimal compression of the dictionary, which is O(km).  ...  Its time complexity is linear in the size of the text with preprocessing time linear in the size of the dictionary.  ... 
doi:10.1007/978-3-642-13509-5_4 fatcat:5bh3sc3woneqtlbnhvhi7wlxim

Succinct 2D Dictionary Matching

Shoshana Neuburger, Dina Sokol
2012 Algorithmica  
The time complexity of our algorithm is close to linear, O(dm 2 + n 2 τ log σ ), where τ is the time it takes to access a character in the compressed self-index and σ is the size of the alphabet.  ...  This paper presents the first efficient 2-dimensional dictionary matching algorithm that operates in small space.  ...  This work has been supported in part by the National Science Foundation Grant BD&I 0542751 and the Professional Staff Congress-City University of New York Research Award 63343-0041.  ... 
doi:10.1007/s00453-012-9615-9 fatcat:v2a5t42otfcc5oz6osg4nw5tsa

Efficiently computing runs on a trie [article]

Ryo Sugahara, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda
2021 arXiv   pre-print
Furthermore, we also show an O(nloglog n) time and O(n) space algorithm for finding all runs.  ...  We also show an asymptotic lower bound on the maximum density of runs in tries: lim_n→∞ρ_𝒯(n)/n ≥ 0.993238 where ρ_𝒯(n) is the maximum number of runs in a trie with n edges.  ...  From Lemma 3, the longest Lyndon word starting at each position of a string w can be computed in linear time, given the inverse suffix array of w.  ... 
arXiv:1901.10633v3 fatcat:4d4sgehqb5d37ip72o2wbvljf4

Computing minimal and maximal suffixes of a substring

Maxim Babenko, Paweł Gawrychowski, Tomasz Kociumaka, Ignat Kolesnichenko, Tatiana Starikovskaya
2016 Theoretical Computer Science  
As a sample application, we show that this data structure can be used to compute the Lyndon decomposition of any substring of the text in O(kτ ) time, where k is the number of distinct factors in the decomposition  ...  For the maximal suffix problem, we give a linear-space structure with O(1) query time and O(n) preprocessing time.  ...  The suffix tree of a string can be constructed in linear time and occupies linear space. Once constructed, it allows to retrieve the maximal and the minimal suffixes in constant time.  ... 
doi:10.1016/j.tcs.2015.08.023 fatcat:wutx6cblkbaplokcp56wtsb4ea
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