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Linear Time Algorithm for the Longest Common Repeat Problem
[chapter]
2004
Lecture Notes in Computer Science
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We also consider reversed and reverse-complemented 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. ...
doi:10.1007/978-3-540-30213-1_2
fatcat:e5nqq2fbhrcitpzok3zgdnty5a
Linear time algorithm for the longest common repeat problem
2007
Journal of Discrete Algorithms
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We also consider reversed and reverse-complemented 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. ...
doi:10.1016/j.jda.2006.03.019
fatcat:gwc4vuy5bjfu7ipo4e4q2aogia
The Labeled Direct Product Optimally Solves String Problems on Graphs
[article]
2021
arXiv
pre-print
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simpler 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 ...
arXiv:2109.05290v1
fatcat:d7oc5sldinaurlja4k75gzwq4a
Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis
2012
Algorithms for Molecular Biology
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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. ...
doi:10.1186/1748-7188-7-10
pmid:22551152
pmcid:PMC3402988
fatcat:tx2vjewa2nfmbmuax64naohedq
Subject Index
2007
Journal of Discrete Algorithms
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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 ...
doi:10.1016/s1570-8667(07)00076-7
fatcat:wfqxglrznfb6do3wyittd5pfbi
Exact Tandem Repeats using Suffix Array and Longest Common Prefix
2018
Helix
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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. ...
doi:10.29042/2018-3686-3691
fatcat:4rbfd3rbgjdh7gcfjsjwfdy42m
Efficient repeat finding in sets of strings via suffix arrays
2013
Discrete Mathematics & Theoretical Computer Science
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Discrete 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. ...
doi:10.46298/dmtcs.597
fatcat:dc2tkatjsjgafp2ndwj2wuvlry
Suffix Trees and Suffix Arrays
[chapter]
2004
Handbook of Data Structures and Applications
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A similar proof shows that this 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. ...
doi:10.1201/9781420035179.ch29
fatcat:3fjsu4q2cnfjngceepvgij3uvi
2004 Symposium on String Processing and Information Retrieval
2007
Journal of Discrete Algorithms
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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. ...
doi:10.1016/j.jda.2006.03.016
fatcat:xh6qy7tqcff5toelhmpzrkqnlu
Longest repeats with a block of k don't cares
2006
Theoretical Computer Science
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We propose an O(n log n)-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. ...
doi:10.1016/j.tcs.2006.06.029
fatcat:yp25joksdbf4bjawh3q3hoxure
Subject Index
2004
Journal of Discrete Algorithms
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on 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 ...
doi:10.1016/s1570-8667(04)00076-0
fatcat:3igwdxr5pba53eev4y6a2jzgie
Longest Gapped Repeats and Palindromes
[chapter]
2015
Lecture Notes in Computer Science
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We show how to compute efficiently, 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 ...
doi:10.1007/978-3-662-48057-1_16
fatcat:ptzozpf72vdvtcsgrzl45srpnm
Longest Gapped Repeats and Palindromes
[article]
2017
arXiv
pre-print
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We show how to compute efficiently, 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 ...
arXiv:1511.07180v3
fatcat:5khsncio4ffj7mzsq3bjglzjta
SA-SSR: a suffix array-based algorithm for exhaustive and efficient SSR discovery in large genetic sequences: Table 1
2016
Bioinformatics
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Here, we present an innovative 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. ...
doi:10.1093/bioinformatics/btw298
pmid:27170037
pmcid:PMC5013907
fatcat:hv2vvfwoajfhzmx6aei6z2uene
An Efficient Algorithm for the Longest Tandem Scattered Subsequence Problem
[chapter]
2004
Lecture Notes in Computer Science
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An efficient 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. ...
doi:10.1007/978-3-540-30213-1_13
fatcat:meh6fzj6rvfq3bjrczlxix6oiq
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