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On stabbing queries for generalised longest repeats

2016
*
International Journal of Data Mining and Bioinformatics
*

Further, our solution can find all

doi:10.1504/ijdmb.2016.078152
fatcat:mnbiwuurubgd7cgfojl7ffygme
*longest**repeats*covering any given interval using optimal O(occ)*time*, where occ is*the*number of*longest**repeats*covering that given interval. ... In this paper, we extend*the*point query to interval query, allowing*the*search*for**longest**repeat*(s) covering any position interval. ... Queries on Strings (Hu et al., 2014) at an early stage, which sparked*the*idea of*the**problem*and its solution presented in this paper. ...##
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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. ...##
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Distributed suffix trees

2005
*
Journal of Discrete Algorithms
*

*The*method is based on a new

*linear*

*time*construction

*algorithm*

*for*subtrees of a suffix tree. ...

*The*new data structure tackles

*the*memory bottleneck

*problem*by constructing these subtrees independently and in parallel. ... To construct

*the*DST in

*linear*

*time*we show how to construct an SST in

*linear*

*time*and simply run

*the*

*algorithm*in parallel

*for*

*the*different prefixes that are chosen. ...

##
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Longest Common Prefixes with k-Errors and Applications
[chapter]

2018
*
Lecture Notes in Computer Science
*

Our first result is an improvement upon

doi:10.1007/978-3-030-00479-8_3
fatcat:2xhap3e2xfaihggp3p4ai365fa
*the*state-of-*the*-art average-case*time*complexity*for*non-constant k and using only*linear*space under*the*Hamming distance model. ... In this paper, we study*the**problem*of computing*the**longest*prefix of each suffix of a given string of length n over a constantsized alphabet that occurs elsewhere in*the*string with k-errors. ... Other related works: In [14] it was shown that a strongly subquadratic-*time**algorithm**for**the**longest**common*substring with k-errors*problem*,*for*k = Ω(log n) and binary strings, refutes*the*Strong Exponential ...##
###
Longest Common Prefixes with k-Mismatches and Applications
[chapter]

2017
*
Lecture Notes in Computer Science
*

We propose a new

doi:10.1007/978-3-319-73117-9_45
fatcat:hbv7epxf5zbzzl6pjs4wsug42y
*algorithm**for*computing*the**longest*prefix of each suffix of a given string of length n over a constant-sized alphabet of size σ that occurs elsewhere in*the*string with Hamming distance ... This improves upon*the*state-of-theart average-case*time*complexity*for**the*case when k = 1 [Manzini, SPIRE 2015] by a factor of log n/ log 3 log n. ... A*time*-space optimal (*linear*)*algorithm*that computes*the*LPF array is known*for*some*time*[10] . ...##
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Testing Generalised Freeness of Words

2014
*
Symposium on Theoretical Aspects of Computer Science
*

ACM Subject Classification F.2.2 Nonnumerical

doi:10.4230/lipics.stacs.2014.337
dblp:conf/stacs/GawrychowskiMN14
fatcat:z2k57sxbgfbr7bnchlfemqu67u
*Algorithms*and*Problems*... Pseudo-repetitions are a natural*generalisation*of*the*classical notion of repetitions in sequences: they are*the**repeated*concatenation of a word and its encoding under a certain morphism or antimorphism ...*The*main question left open is whether*the*results reported here can be improved to find (if there exist)*algorithmic*solutions*for**the*approached*problems*running in O(n)*time*. ...##
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Superstring Graph: A New Approach for Genome Assembly
[chapter]

2016
*
Lecture Notes in Computer Science
*

In

doi:10.1007/978-3-319-41168-2_4
fatcat:cns7emg7tvcuvmeptkn746jlye
*linear**time*and space, it combines*the*efficiency of a greedy approach to*the*advantages of using a single graph. ... Overlap graph based*algorithms*were used with*the*first generation of sequencers, while de Bruijn graph (DBG) based methods were preferred*for**the*second generation. ... We thank*the*reviewers*for*their comments and suggestions. ...##
###
Homology and linkage in crossover for linear genomes of variable length

2019
*
PLoS ONE
*

Here, we revisit crossover

doi:10.1371/journal.pone.0209712
pmid:30605463
pmcid:PMC6317799
fatcat:2ng22m3t4vdbvlwifdolfegr5q
*for**linear*genomes of variable length, identifying two crucial attributes of successful recombination*algorithms*:*the*ability to retain homologous structure, and to reshuffle ... In addition, we measure*the*performance of these crossover methods on three different benchmark*problems*, and find that variable-length genomes out-perform fixed-length variants in all three cases. ... Acknowledgments We are grateful to Karl Fogelmark*for*interesting discussions and Carsten Peterson*for*comments and encouragement. ...##
###
Time–space trade-offs for longest common extensions

2014
*
Journal of Discrete Algorithms
*

We study

doi:10.1016/j.jda.2013.06.003
fatcat:tyahwybryvb7rlbgtclx6bgcwq
*the**time*-space trade-offs*for**the**problem*, that is,*the*space used*for**the*data structure vs.*the*worst-case*time**for*answering an LCE query. Let n be*the*length of T . ... We revisit*the**longest**common*extension (LCE)*problem*, that is, preprocess a string T into a compact data structure that supports fast LCE queries. ... Acknowledgements We thank*the*anonymous referes*for*their valuable comments, and in particular*for*pointing out an issue with*the*preprocessing space of*the*randomised solution. ...##
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A linear time algorithm for Shortest Cyclic Cover of Strings

2016
*
Journal of Discrete Algorithms
*

SCCS is used as a crucial step in polynomial

doi:10.1016/j.jda.2016.05.001
fatcat:3azou2obczffjpwcge7nh6jjj4
*time*approximation*algorithms**for**the*notably hard Shortest Superstring*problem*, but it is solved in cubic*time*. ... Here, we propose a*linear**time**algorithm**for*solving SCCS based on a Eulerian graph that captures all greedy solutions in*linear*space. ...*The*minimisation of*the*number of cyclic strings by*Algorithm*3 is illustrated in Fig. 7 . Theorem 7.*Algorithm*3 solves*Problem*2 in*linear**time*. Proof. ...##
###
Fast distance multiplication of unit-Monge matrices
[chapter]

2010
*
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
*

We also gave a distance multiplication

doi:10.1137/1.9781611973075.103
dblp:conf/soda/Tiskin10
fatcat:2kpawne2qne4rofcckuge22pbq
*algorithm**for*such matrices, running in*time*O(n 1.5 ). Landau asked whether this*problem*can be solved in*linear**time*. ...*The*new*algorithm*implies immediate improvements in running*time**for*a number of*algorithms*on strings and graphs. ...*Algorithmic*applications*The**longest**common*subsequence (LCS)*problem*is a classical*problem*in computer science. ...##
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Fast Distance Multiplication of Unit-Monge Matrices

2013
*
Algorithmica
*

We also gave a distance multiplication

doi:10.1007/s00453-013-9830-z
fatcat:pechvfjw2vbarfqa3oemqh3t6q
*algorithm**for*such matrices, running in*time*O(n 1.5 ). Landau asked whether this*problem*can be solved in*linear**time*. ...*The*new*algorithm*implies immediate improvements in running*time**for*a number of*algorithms*on strings and graphs. ...*Algorithmic*applications*The**longest**common*subsequence (LCS)*problem*is a classical*problem*in computer science. ...##
###
Time-Space Trade-Offs for Longest Common Extensions
[chapter]

2012
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/978-3-642-31265-6_24
fatcat:puexhxxzjnfjpmhda3qtbhsm6m
*the**time*-space trade-offs*for**the**problem*, that is,*the*space used*for**the*data structure vs.*the*worst-case*time**for*answering an LCE query. Let n be*the*length of T . ... We revisit*the**longest**common*extension (LCE)*problem*, that is, preprocess a string T into a compact data structure that supports fast LCE queries. ... Acknowledgements We thank*the*anonymous referes*for*their valuable comments, and in particular*for*pointing out an issue with*the*preprocessing space of*the*randomised solution. ...##
###
Generalised k-Steiner Tree Problems in Normed Planes

2013
*
Algorithmica
*

We show that,

doi:10.1007/s00453-013-9780-5
fatcat:hsoebwee55hopncq53g7ony6h4
*for*any fixed k, such*problems*can be solved in O(n^2k)*time*. ... Their*algorithm*produces an optimal solution within O(n^2)*time*. ... Hence,*for**the*power-p Steiner tree*problem*we define α(e T ,X,S ) = α p (e T ,X,S ) := n+k −1 i=1 e i p ; whereas,*for**the*bottleneck*problem*(where*the*cost of*the*network is*the*cost of*the**longest*...##
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A Unified Methodology for the Generalisation of the Geometry of Features

2021
*
ISPRS International Journal of Geo-Information
*

It also consists of

doi:10.3390/ijgi10030107
fatcat:yflpbcmqrndg7cknmmgaqk35ry
*the*assessment of results from*the**algorithms*, i.e., characteristics that are indispensable*for*automatic*generalisation*. ...*The*preparation of a fully automatic*generalisation**for*spatial data requires certain standards, as well as unique and verifiable*algorithms**for*particular groups of features. ...*The*paper presents a new solution*for*digital automatic cartographic*generalisation**for**the*geometry of*linear*and areal objects. ...
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