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

Inbok Lee, Costas S. Iliopoulos, Kunsoo Park
2004 Lecture Notes in Computer Science  
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

Inbok Lee, Costas S. Iliopoulos, Kunsoo Park
2007 Journal of Discrete Algorithms  
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]

Nicola Rizzo, Alexandru I. Tomescu, Alberto Policriti
2021 arXiv   pre-print
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

Susana Vinga, Alexandra M Carvalho, Alexandre P Francisco, Luís MS Russo, Jonas S Almeida
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.  ... 
doi:10.1186/1748-7188-7-10 pmid:22551152 pmcid:PMC3402988 fatcat:tx2vjewa2nfmbmuax64naohedq

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  ... 
doi:10.1016/s1570-8667(07)00076-7 fatcat:wfqxglrznfb6do3wyittd5pfbi

Exact Tandem Repeats using Suffix Array and Longest Common Prefix

Raju Bhukya
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.  ... 
doi:10.29042/2018-3686-3691 fatcat:4rbfd3rbgjdh7gcfjsjwfdy42m

Efficient repeat finding in sets of strings via suffix arrays

Pablo Barenbaum, Verónica Becher, Alejandro Deymonnaz, Melisa Halsband, Pablo Ariel Heiber
2013 Discrete Mathematics & Theoretical Computer Science  
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]

Srinivas Aluru
2004 Handbook of Data Structures and Applications  
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

Alberto Apostolico, Ricardo Baeza-Yates, Massimo Melucci
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.  ... 
doi:10.1016/j.jda.2006.03.016 fatcat:xh6qy7tqcff5toelhmpzrkqnlu

Longest repeats with a block of k don't cares

Maxime Crochemore, Costas S. Iliopoulos, Manal Mohamed, Marie-France Sagot
2006 Theoretical Computer Science  
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  
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]

Marius Dumitran, Florin Manea
2015 Lecture Notes in Computer Science  
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]

Marius Dumitran, Paweł Gawrychowski, Florin Manea
2017 arXiv   pre-print
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

B. D. Pickett, S. M. Karlinsey, C. E. Penrod, M. J. Cormier, M. T. W. Ebbert, D. K. Shiozawa, C. J. Whipple, P. G. Ridge
2016 Bioinformatics  
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]

Adrian Kosowski
2004 Lecture Notes in Computer Science  
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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