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## Filters

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Computing the Cover Array in Linear Time

2002
*
Algorithmica
*

##
###
On left and right seeds of a string

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] . ...

##
###
Efficient Seeds Computation Revisited
[article]

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. ...

##
###
Efficient Seeds Computation Revisited
[chapter]

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*...

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

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] . ...

##
###
Computing Covers Using Prefix Tables
[article]

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*. ...

##
###
Efficient seed computation revisited

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. ...

##
###
Computing covers using prefix tables

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*. ...

##
###
Cover Array String Reconstruction
[chapter]

2010
*
Lecture Notes in Computer Science
*

Minimal/Maximal

doi:10.1007/978-3-642-13509-5_23
fatcat:vim2qvkvufhbhedk44dqrw6jum
*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*...##
###
Simple Linear Work Suffix Array Construction
[chapter]

2003
*
Lecture Notes in Computer Science
*

We introduce

doi:10.1007/3-540-45061-0_73
fatcat:5l6a3kvv5fandemcha7yi4gj6e
*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*. ...##
###
Computing regularities in strings: A survey

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*. ...

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

2015
*
arXiv
*
pre-print

Both for regular and indeterminate strings, our algorithms execute

arXiv:1506.06793v1
fatcat:knlzkaozczf3jassdljw4vnn6i
*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 ...##
###
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]

2003
*
Lecture Notes in Computer Science
*

We describe an algorithm that, for any v ∈ [2, n], constructs

doi:10.1007/3-540-44888-8_5
fatcat:gnic25jlz5hgzll3in4ez35weu
*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*. ...##
###
Linear work suffix array construction

2006
*
Journal of the ACM
*

For any v ∈ [1, √ n], it runs

doi:10.1145/1217856.1217858
fatcat:icwh6toiwvfqbm3xot6obq4rqa
*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*. ...
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