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On stabbing queries for generalised longest repeats

Bojian Xu
2016 International Journal of Data Mining and Bioinformatics  
Further, our solution can find all 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.  ... 
doi:10.1504/ijdmb.2016.078152 fatcat:mnbiwuurubgd7cgfojl7ffygme

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

Distributed suffix trees

Raphaël Clifford
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.  ... 
doi:10.1016/j.jda.2004.08.004 fatcat:6mnw675kerdffejam6ykkqmwc4

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

Lorraine A. K. Ayad, Carl Barton, Panagiotis Charalampopoulos, Costas S. Iliopoulos, Solon P. Pissis
2018 Lecture Notes in Computer Science  
Our first result is an improvement upon 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  ... 
doi:10.1007/978-3-030-00479-8_3 fatcat:2xhap3e2xfaihggp3p4ai365fa

Longest Common Prefixes with k-Mismatches and Applications [chapter]

Hayam Alamro, Lorraine A. K. Ayad, Panagiotis Charalampopoulos, Costas S. Iliopoulos, Solon P. Pissis
2017 Lecture Notes in Computer Science  
We propose a new 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] .  ... 
doi:10.1007/978-3-319-73117-9_45 fatcat:hbv7epxf5zbzzl6pjs4wsug42y

Testing Generalised Freeness of Words

Pawel Gawrychowski, Florin Manea, Dirk Nowotka, Marc Herbstritt
2014 Symposium on Theoretical Aspects of Computer Science  
ACM Subject Classification F.2.2 Nonnumerical 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.  ... 
doi:10.4230/lipics.stacs.2014.337 dblp:conf/stacs/GawrychowskiMN14 fatcat:z2k57sxbgfbr7bnchlfemqu67u

Superstring Graph: A New Approach for Genome Assembly [chapter]

Bastien Cazaux, Gustavo Sacomoto, Eric Rivals
2016 Lecture Notes in Computer Science  
In 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.  ... 
doi:10.1007/978-3-319-41168-2_4 fatcat:cns7emg7tvcuvmeptkn746jlye

Homology and linkage in crossover for linear genomes of variable length

Adriaan Merlevede, Henrik Åhl, Carl Troein, Denis Horvath
2019 PLoS ONE  
Here, we revisit crossover 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.  ... 
doi:10.1371/journal.pone.0209712 pmid:30605463 pmcid:PMC6317799 fatcat:2ng22m3t4vdbvlwifdolfegr5q

Time–space trade-offs for longest common extensions

Philip Bille, Inge Li Gørtz, Benjamin Sach, Hjalte Wedel Vildhøj
2014 Journal of Discrete Algorithms  
We study 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.  ... 
doi:10.1016/j.jda.2013.06.003 fatcat:tyahwybryvb7rlbgtclx6bgcwq

A linear time algorithm for Shortest Cyclic Cover of Strings

Bastien Cazaux, Eric Rivals
2016 Journal of Discrete Algorithms  
SCCS is used as a crucial step in polynomial 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.  ... 
doi:10.1016/j.jda.2016.05.001 fatcat:3azou2obczffjpwcge7nh6jjj4

Fast distance multiplication of unit-Monge matrices [chapter]

Alexander Tiskin
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
We also gave a distance multiplication 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.  ... 
doi:10.1137/1.9781611973075.103 dblp:conf/soda/Tiskin10 fatcat:2kpawne2qne4rofcckuge22pbq

Fast Distance Multiplication of Unit-Monge Matrices

Alexander Tiskin
2013 Algorithmica  
We also gave a distance multiplication 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.  ... 
doi:10.1007/s00453-013-9830-z fatcat:pechvfjw2vbarfqa3oemqh3t6q

Time-Space Trade-Offs for Longest Common Extensions [chapter]

Philip Bille, Inge Li Gørtz, Benjamin Sach, Hjalte Wedel Vildhøj
2012 Lecture Notes in Computer Science  
We study 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.  ... 
doi:10.1007/978-3-642-31265-6_24 fatcat:puexhxxzjnfjpmhda3qtbhsm6m

Generalised k-Steiner Tree Problems in Normed Planes

Marcus Brazil, Charl J. Ras, Konrad J. Swanepoel, Doreen A. Thomas
2013 Algorithmica  
We show that, 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  ... 
doi:10.1007/s00453-013-9780-5 fatcat:hsoebwee55hopncq53g7ony6h4

A Unified Methodology for the Generalisation of the Geometry of Features

Anna Barańska, Joanna Bac-Bronowicz, Dorota Dejniak, Stanisław Lewiński, Artur Krawczyk, Tadeusz Chrobak
2021 ISPRS International Journal of Geo-Information  
It also consists of 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.  ... 
doi:10.3390/ijgi10030107 fatcat:yflpbcmqrndg7cknmmgaqk35ry
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