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Computing the Cover Array in Linear Time

Li, Smyth
2002 Algorithmica  
doi:10.1007/s00453-001-0062-2 fatcat:gskkb4b3pbavlolnupjewqr34i

On left and right seeds of a string

Michalis Christou, Maxime Crochemore, Ondrej Guth, Costas S. Iliopoulos, Solon P. Pissis
2012 Journal of Discrete Algorithms  
In this article, we present linear-time algorithms for computing all left and right seeds of y, a linear-time algorithm for computing the minimal left-seed array of y, a linear-time solution for computing  ...  the maximal left-seed array of y, an O(n log n)-time algorithm for computing the minimal right-seed array of y, and a linear-time solution for computing the maximal right-seed array of y.  ...  The proposed algorithm uses the linear-time algorithm for computing the maximal cover array C M [18] and the linear-time algorithm for computing the period array P [16] .  ... 
doi:10.1016/j.jda.2012.10.004 fatcat:opxiha2s3fdsjoqgjy6xf6zonq

Efficient Seeds Computation Revisited [article]

Michalis Christou, Maxime Crochemore, Costas S. Iliopoulos, Marcin Kubica, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Bartosz Szreder, Tomasz Walen
2011 arXiv   pre-print
In the paper we give linear time algorithms for some of its versions --- computing shortest left-seed array, longest left-seed array and checking for seeds of a given length.  ...  The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in O(n^2) time.  ...  We start by sorting LL(root (T )), which can be done in O(n) time. Throughout the algorithm we store a global auxiliary array pos[1 . . n], required in the ChainPrefixMaxgap algorithm.  ... 
arXiv:1104.3153v1 fatcat:xebkhlwo7zepzjdiveemjrgqt4

Efficient Seeds Computation Revisited [chapter]

Michalis Christou, Maxime Crochemore, Costas S. Iliopoulos, Marcin Kubica, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Bartosz Szreder, Tomasz Waleń
2011 Lecture Notes in Computer Science  
In the paper we give linear time algorithms for some of its versions -computing shortest left-seed array, longest left-seed array and checking for seeds of a given length.  ...  The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover.  ...  Algorithm Alternative-ComputeLeftSeedArray runs in linear time. Proof. Recall that the arrays P[1 . . n] and C[1 . . n] can be computed in linear time  ... 
doi:10.1007/978-3-642-21458-5_30 fatcat:lfag6gzroncblhw3r3mjoprmam

Linear Time Inference of Strings from Cover Arrays using a Binary Alphabet [article]

Tanaeem M. Moosa, Sumaiya Nazeen, M. Sohel Rahman, Rezwana Reaz
2011 arXiv   pre-print
In this paper, we focus on the problem of linear time inference of strings from cover arrays using the least sized alphabet possible.  ...  This algorithm uses several interesting combinatorial properties of cover arrays and an interesting relation between border array and cover array to achieve this. Our algorithm runs in linear time.  ...  This computation is linear in the number of edges which is bounded by 2n. Also the overall on-line computation of the border array B runs in linear time [2] .  ... 
arXiv:1108.5422v1 fatcat:wj6t6so6kjawvd3r3easnjnjym

Computing Covers Using Prefix Tables [article]

Ali Alatabbi and M. Sohel Rahman and W. F. Smyth
2015 arXiv   pre-print
In this paper we first describe a linear-time algorithm to compute the cover array of regular string x based on the prefix table of x. We then extend this result to indeterminate strings.  ...  Fifteen years ago a complex, though nevertheless linear-time, algorithm was proposed to compute the cover array of regular x based on prior computation of the border array of x.  ...  is, each can be computed from x in linear time, and each can be computed from the other, without reference to x, also in linear time.  ... 
arXiv:1412.3016v2 fatcat:4gm4cvsv3jg2zeqe7lhmtbzz2q

Efficient seed computation revisited

M. Christou, M. Crochemore, C.S. Iliopoulos, M. Kubica, S.P. Pissis, J. Radoszewski, W. Rytter, B. Szreder, T. Waleń
2013 Theoretical Computer Science  
The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in O(n 2 ) time.  ...  In the paper we give linear time algorithms for some of its versionscomputing shortest left-seed array, longest left-seed array and checking for seeds of a given length.  ...  N206 568540 of the National Science Centre. Wojciech Rytter is supported by grant no. N206 566740 of the National Science Centre.  ... 
doi:10.1016/j.tcs.2011.12.078 fatcat:dfuffpt4hfagdbtcfmocawrtra

Computing covers using prefix tables

Ali Alatabbi, M. Sohel Rahman, W.F. Smyth
2016 Discrete Applied Mathematics  
In this paper we first describe a linear-time algorithm to compute the cover array of regular x based on the prefix table of x. We then extend this result to indeterminate strings.  ...  Fifteen years ago a complex, though nevertheless linear-time, algorithm was proposed to compute the cover array of regular x based on prior computation of the border array of x.  ...  is, each can be computed from x in linear time, and each can be computed from the other, without reference to x, also in linear time.  ... 
doi:10.1016/j.dam.2015.05.019 fatcat:jugsoqzp35fgpj7pdyk6qmfcgm

Cover Array String Reconstruction [chapter]

Maxime Crochemore, Costas S. Iliopoulos, Solon P. Pissis, German Tischler
2010 Lecture Notes in Computer Science  
Minimal/Maximal Cover If y has a cover, then it has a unique minimal (shortest) and maximal (longest) cover. Cover Array String Reconstruction (3/26)  ...  Cover A proper factor u of y (i.e. a factor u of y s.t. u = y) is a cover (or quasiperiod) of y, iff every position of y lies in an occurence of u in y.  ...  Smyth, Computing the Cover Array in Linear Time, Algorithmica 32 1 (2002), pp. 95-106) Cover Array String Reconstruction (5/26) Example (Cover array)The following table provides the minimal-cover array  ... 
doi:10.1007/978-3-642-13509-5_23 fatcat:vim2qvkvufhbhedk44dqrw6jum

Simple Linear Work Suffix Array Construction [chapter]

Juha Kärkkäinen, Peter Sanders
2003 Lecture Notes in Computer Science  
We introduce the skew algorithm for suffix array construction over integer alphabets that can be implemented to run in linear time using integer sorting as its only nontrivial subroutine: 1. recursively  ...  A suffix array represents the suffixes of a string in sorted order.  ...  There is a linear time algorithm for computing the lcp array from the suffix array [27] , but it does not appear to be suitable for parallel or external computation.  ... 
doi:10.1007/3-540-45061-0_73 fatcat:5l6a3kvv5fandemcha7yi4gj6e

Computing regularities in strings: A survey

W.F. Smyth
2013 European journal of combinatorics (Print)  
The aim of this survey is to provide insight into the sequential algorithms that have been proposed to compute exact "regularities" in strings; that is, covers (or quasiperiods), seeds, repetitions, runs  ...  After outlining and evaluating the algorithms that have been proposed for their computation, I suggest possibly productive future directions of research.  ...  , be computed in linear time.  ... 
doi:10.1016/j.ejc.2012.07.010 fatcat:4vdmvekfpngu3csv4zbz5sa4jy

Enhanced Covers of Regular & Indeterminate Strings using Prefix Tables [article]

Ali Alatabbi, A. S. Sohidull Islam, M. Sohel Rahman, Jamie Simpson and W. F. Smyth
2015 arXiv   pre-print
Both for regular and indeterminate strings, our algorithms execute in expected linear time.  ...  In this paper, we first show how to compute enhanced covers using instead the prefix table: an array π[1..n] such that π[i] is the length of the longest substring of x beginning at position i that matches  ...  Several linear-time algorithms were proposed for the computation of covers [4, 8, 17, 18] , culminating in an algorithm [16] to compute the cover array γ, where γ[i] gives the length j of the longest  ... 
arXiv:1506.06793v1 fatcat:knlzkaozczf3jassdljw4vnn6i

Page 2143 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
Author summary (translated from the Russian): “We consider the flow of computational schemes for the solution of a number of problems of linear algebra, taking into account the space-time peculiarities  ...  V. (1-MD-C); 86e:65181 Varman, Peter J. (1-RICE) Modular matrix multiplication on a linear array. IEEE Trans. Comput. 33 (1984), no. 11, 952-958.  ... 

Fast Lightweight Suffix Array Construction and Checking [chapter]

Stefan Burkhardt, Juha Kärkkäinen
2003 Lecture Notes in Computer Science  
We describe an algorithm that, for any v ∈ [2, n], constructs the suffix array of a string of length n in O(vn space in addition to the input (the string) and the output (the suffix array).  ...  The key idea of the algorithm is to first sort a sample of suffixes chosen using mathematical constructs called difference covers.  ...  Previous suffix array construction algorithms can be classified into four main categories. The algorithms in the first category compute the suffix array from the suffix tree in linear time.  ... 
doi:10.1007/3-540-44888-8_5 fatcat:gnic25jlz5hgzll3in4ez35weu

Linear work suffix array construction

Juha Kärkkäinen, Peter Sanders, Stefan Burkhardt
2006 Journal of the ACM  
For any v ∈ [1, √ n], it runs in O(vn) time using O(n/ √ v) space in addition to the input string and the suffix array.  ...  We narrow this gap between theory and practice with a simple linear-time construction algorithm for suffix arrays.  ...  There are simple linear time algorithms for computing the lcp array from the suffix array [38, 46] , but they do not appear to be suitable for parallel or external computation.  ... 
doi:10.1145/1217856.1217858 fatcat:icwh6toiwvfqbm3xot6obq4rqa
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