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Linear Time Algorithm for the Longest Common Repeat Problem
[chapter]

2004
*
Lecture Notes in Computer Science
*

We also consider reversed and reverse-complemented

doi:10.1007/978-3-540-30213-1_2
fatcat:e5nqq2fbhrcitpzok3zgdnty5a
*repeats*as well as normal*repeats*. We present a*linear**time**algorithm**for**the**longest**common**repeat**problem*. ... . , T },*the**longest**common**repeat**problem*is to find*the**longest**common*substring that appears at least twice in each string of U . ... a*linear**time**algorithm**for**the**problem*, allowing reversed and reverse-complemented*repeats*. ...##
###
Linear time algorithm for the longest common repeat problem

2007
*
Journal of Discrete Algorithms
*

We also consider reversed and reverse-complemented

doi:10.1016/j.jda.2006.03.019
fatcat:gwc4vuy5bjfu7ipo4e4q2aogia
*repeats*as well as normal*repeats*. We present a*linear**time**algorithm**for**the**longest**common**repeat**problem*. ... . , T },*the**longest**common**repeat**problem*is to find*the**longest**common*substring that appears at least twice in each string of U . ... a*linear**time**algorithm**for**the**problem*, allowing reversed and reverse-complemented*repeats*. ...##
###
The Labeled Direct Product Optimally Solves String Problems on Graphs
[article]

2021
*
arXiv
*
pre-print

simpler

arXiv:2109.05290v1
fatcat:d7oc5sldinaurlja4k75gzwq4a
*algorithms**for**the*quadratic*problems*of string matching (SMLG) and*longest**common*substring (LCSP) in labeled graphs. ... Our*algorithms*are also more efficient, since they run in*time**linear*in*the*size of*the*labeled product graph, which may be smaller than quadratic*for*some inputs, and their run-*time*is predictable, because ... Acknowledgments We are very grateful to Roberto Grossi,*for*initial discussions on*the**longest**repeated*string*problem*that spurred this line of research, and to Veli Mäkinen and Massimo Equi*for*their ...##
###
Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis

2012
*
Algorithms for Molecular Biology
*

*The*

*common*feature of these

*problems*is that they use

*longest*

*common*extension (LCE) queries as subtasks of their procedures, which we show to have a constant

*time*solution with CGR. ... a unifying analytical framework

*for*a diversity of pattern matching

*problems*. ...

*the*

*longest*

*common*substring

*problem*. ...

##
###
Subject Index

2007
*
Journal of Discrete Algorithms
*

*time*

*algorithm*

*for*

*the*

*longest*

*common*

*repeat*

*problem*, 243 Generating function Failed disk recovery in double erasure RAID arrays, 115 Genome rearrangements A

*linear*

*time*

*algorithm*

*for*

*the*inversion ... in wireless networks, 395

*Linear*

*time*

*algorithm*

*for*

*the*

*longest*

*common*

*repeat*

*problem*, 243; An upper bound on

*the*hardness of exact matrix based motif discovery, 706 String matching Parameterized matching ...

##
###
Exact Tandem Repeats using Suffix Array and Longest Common Prefix

2018
*
Helix
*

*The*proposed

*algorithm*reported exact tandem

*repeats*with a motif length of at least three 3 with

*the*help of an

*algorithm*that uses a suffix array and

*longest*

*common*prefix. ... Tandem

*Repeats*(TRs) are

*the*

*repeats*which occur in a chromosome, while a pattern of 1 or more nucleotides (A, C, G, T) is

*repeated*more than one

*time*and

*the*repetitions are continuous. ... Construction of LCPA from Suffix array also takes

*linear*

*time*O(n). Dynamic arrays were used in

*the*construction of suffix array and

*longest*

*common*prefix array. ...

##
###
Efficient repeat finding in sets of strings via suffix arrays

2013
*
Discrete Mathematics & Theoretical Computer Science
*

Discrete

doi:10.46298/dmtcs.597
fatcat:dc2tkatjsjgafp2ndwj2wuvlry
*Algorithms*International audience We consider two*repeat*finding*problems*relative to sets of strings: (a) Find*the*largest substrings that occur in every string of a given set; (b) Find*the*maximal ... Our solutions are based on*the*suffix array construction, requiring O(m) memory, where m is*the*length of*the**longest*input string, and O(n &log;m)*time*, where n is*the**the*whole input size (*the*sum of ... Acknowledgments We thank*the*anonymous referees*for*their comments and suggestions.*The*group has received support from Biosidus and IBM Argentina. ...##
###
Suffix Trees and Suffix Arrays
[chapter]

2004
*
Handbook of Data Structures and Applications
*

A similar proof shows that this

doi:10.1201/9781420035179.ch29
fatcat:3fjsu4q2cnfjngceepvgij3uvi
*algorithm*runs in O(m + n)*time*. Now consider solving*the**longest**common*substring*problem*using*the*GSA and Lcp array*for*strings s 1 and s 2 . ... Any consecutive pair of such leaves have*the**longest**repeat*as their*longest**common*prefix. Thus, each largest value in*the*Lcp array reveals a*longest**repeat*in*the*string. ...##
###
2004 Symposium on String Processing and Information Retrieval

2007
*
Journal of Discrete Algorithms
*

*The*fourth and last paper, by Lee, Iliopoulos and Park, presents a

*linear*

*time*

*algorithm*

*for*

*the*"

*longest*

*common*

*repeat*"

*problem*. ... In

*the*third paper, Iliopoulos, Perdikuri, Theodoridis, Tsakalidis and Tsichlas design three

*algorithms*

*for*motif identification in weighted biological sequences. ...

*The*fourth and last paper, by Lee, Iliopoulos and Park, presents a

*linear*

*time*

*algorithm*

*for*

*the*"

*longest*

*common*

*repeat*"

*problem*. ...

##
###
Longest repeats with a block of k don't cares

2006
*
Theoretical Computer Science
*

We propose an O(n log n)-

doi:10.1016/j.tcs.2006.06.029
fatcat:yp25joksdbf4bjawh3q3hoxure
*time**algorithm**for*computing all*longest*k-*repeats*in a given string x = x[1..n]. ...*The*proposed*algorithm*uses suffix trees to fulfill this task and relies on*the*ability to answer lowest*common*ancestor queries in constant*time*. ... Acknowledgements*The*authors would like to express their gratitude to*the*referees of*the*Theoretical Computer Science*for*their knowledgeable and constructive comments that much improved*the*paper. ...##
###
Subject Index

2004
*
Journal of Discrete Algorithms
*

on

doi:10.1016/s1570-8667(04)00076-0
fatcat:3igwdxr5pba53eev4y6a2jzgie
*the*face-centered- cubic lattice (FCC), 161*Linear*-*time**algorithm*Compact directed acyclic word graphs*for*a slid- ing window, 33*Longest**common*subsequence*The**longest**common*subsequence*problem*...*longest**common*subsequence*problem**for*arc-annotated sequences, 257 Maximum independent set*The**longest**common*subsequence*problem**for*arc-annotated sequences, 257 Median Budget constrained minimum ...##
###
Longest Gapped Repeats and Palindromes
[chapter]

2015
*
Lecture Notes in Computer Science
*

We show how to compute efficiently,

doi:10.1007/978-3-662-48057-1_16
fatcat:ptzozpf72vdvtcsgrzl45srpnm
*for*every position i of*the*word w,*the**longest*gapped*repeat*and palindrome occurring at that position, provided that*the*length of*the*gap is subject to various types ... That is, that*for*each position i we compute*the**longest*prefix u of w[i..n] such that uv (respectively, u R v) is a suffix of w[1..i − 1] (defining thus a gapped*repeat*uvu -respectively, palindrome u ... Acknowledgements*The*authors thank*the*anonymous referees of this paper, as well as those of*the*conference papers which we extend here,*for*their valuable remarks, suggestions, and comments, that improved ...##
###
Longest Gapped Repeats and Palindromes
[article]

2017
*
arXiv
*
pre-print

We show how to compute efficiently,

arXiv:1511.07180v3
fatcat:5khsncio4ffj7mzsq3bjglzjta
*for*every position i of*the*word w,*the**longest*gapped*repeat*and palindrome occurring at that position, provided that*the*length of*the*gap is subject to various types ... That is, that*for*each position i we compute*the**longest*prefix u of w[i..n] such that uv (respectively, u^Rv) is a suffix of w[1..i-1] (defining thus a gapped*repeat*uvu -- respectively, palindrome u^ ... Acknowledgements*The*authors thank*the*anonymous referees of this paper, as well as those of*the*conference papers which we extend here,*for*their valuable remarks, suggestions, and comments, that improved ...##
###
SA-SSR: a suffix array-based algorithm for exhaustive and efficient SSR discovery in large genetic sequences: Table 1

2016
*
Bioinformatics
*

Here, we present an innovative

doi:10.1093/bioinformatics/btw298
pmid:27170037
pmcid:PMC5013907
fatcat:hv2vvfwoajfhzmx6aei6z2uene
*algorithm*, SA-SSR, based on suffix and*longest**common*prefix arrays*for*efficiently detecting SSRs in large sets of sequences. ... SA-SSR is 100% accurate and detected >1000 more SSRs than*the*second best*algorithm*, while offering greater control to*the*user than any existing software. ... Acknowledgements We thank*the*Fulton Supercomputing Laboratory (https://marylou.byu.edu) at Brigham Young University*for*their consistent efforts to support our research. ...##
###
An Efficient Algorithm for the Longest Tandem Scattered Subsequence Problem
[chapter]

2004
*
Lecture Notes in Computer Science
*

An efficient

doi:10.1007/978-3-540-30213-1_13
fatcat:meh6fzj6rvfq3bjrczlxix6oiq
*algorithm**for**the*LTS*problem*is presented and is shown to have O(n 2 ) computational complexity and*linear*memory complexity with respect to*the*length n of*the*analysed sequence. ...*The*paper deals with*the**problem*of finding a tandem scattered subsequence of maximum length (LTS)*for*a given character sequence. ...*The*suggested approach to*the*LT S*problem*reduces LT S*for*sequence s to*the**problem*of determining*the**longest**common*subsequence of two sequences not longer than s. Definition 5. ...
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