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Longest common factor of two words
[chapter]
1987
Lecture Notes in Computer Science
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The LCF of two words u and v is the maximal length of a common factor of u and v. ...
A linear time algorithm to compute LCF is given, based on a linear time algorithm to build the minimal suffix automaton of a word. ...
For instance c lassicalk string-matching algorithms often use a distance related to the longest common prefix of the two strings [KMP 77] . ...
doi:10.1007/3-540-17660-8_45
fatcat:5c6v7p7aezd27kl6d7kjr566me
Avoiding approximate repetitions with respect to the longest common subsequence distance
2016
Involve. A Journal of Mathematics
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In this paper, we show the existence of words avoiding approximate repetitions, where the measure of similarity between adjacent factors is based on the length of the longest common subsequence. ...
An approximate repetition is a factor of the form xx', where x and x' are close to being identical. ...
Here, we measure the closeness of two words based on the length of their longest common subsequence. ...
doi:10.2140/involve.2016.9.657
fatcat:mnfsqn3wkzaidh2xtryxhx2dpy
Longest Lyndon Substring After Edit
2018
Annual Symposium on Combinatorial Pattern Matching
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The longest Lyndon substring of a string T is the longest substring of T which is a Lyndon word. LLS(T ) denotes the length of the longest Lyndon substring of a string T . ...
We can modify our algorithm so as to output all the longest Lyndon substrings of T for both problems. ...
C P M
Longest Common Extension For any string w, the longest common extension query is, given two positions 1 ≤ i, j ≤ |w|, to answer LCE w (i, j) = max{k | w[i..i + k − 1] = w[j..j + k − 1], i + k − ...
doi:10.4230/lipics.cpm.2018.19
dblp:conf/cpm/UrabeNIBT18
fatcat:rikiejsrnfegrn55jajxxab2pu
An Optimal Algorithm for Detecting Pseudo-squares
[chapter]
2006
Lecture Notes in Computer Science
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We consider the problem of determining if a given word, which encodes the boundary of a discrete figure, tiles the plane by translation. ...
These words have been characterized by the Beauquier-Nivat condition, for which we provide a linear time algorithm in the case of pseudo-square polyominoes, improving the previous quadratic algorithm of ...
Our algorithms borrow from Lothaire [11] that the Longest-Common-Factor, the Longest-Common-Prefix and the Longest-Common-Suffix in two words may be computed in linear time. ...
doi:10.1007/11907350_34
fatcat:gb4ep4xdfzgahkhn4mvffvo76i
A note on the longest common substring with k-mismatches problem
[article]
2014
arXiv
pre-print
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The recently introduced longest common substring with k-mismatches (k-LCF) problem is to find, given two sequences S_1 and S_2 of length n each, a longest substring A_1 of S_1 and A_2 of S_2 such that ...
We first present two output-dependent algorithms solving the k-LCF problem and show that for k = O(^1-ε n), where ε > 0, at least one of them works in subquadratic time, using O(n) words of space. ...
Introduction The longest common substring (or factor) problem (LCF) is to find the longest contiguous string shared by two strings S 1 and S 2 , of length n and m, m ≤ n, respectively. W.l.o.g. ...
arXiv:1409.7217v2
fatcat:jmgidjvptfamjiibloq7t6tpse
Searching for gapped palindromes
2009
Theoretical Computer Science
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We study the problem of finding, in a given word, all maximal gapped palindromes verifying two types of constraints, that we call long-armed and length-constrained palindromes. ...
For each of the two classes, we propose an algorithm that runs in time O(n + S) for a constantsize alphabet, where S is the number of output palindromes. ...
Acknowledgments Part of this work was done during the stay of R. Kolpakov ...
doi:10.1016/j.tcs.2009.09.013
fatcat:7ge3eh4a4fg77bhyeg7ltqkyqe
A note on the longest common Abelian factor problem
[article]
2015
arXiv
pre-print
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AILR2015 presented the first solution for the longest common Abelian factor problem for a pair of strings, reaching O(σ n^2) time with O(σ n n) bits of space, where n is the length of the strings and σ ...
In this note we show how the time complexity can be preserved while the space is reduced by a factor of σ, and then how the time complexity can be improved, if the alphabet is not too small, when superlinear ...
We prefer the word "factor" in the problem name, to avoid confusion with the abbreviation for the longest common subsequence. ...
arXiv:1503.01093v3
fatcat:54kkhmaehnbvxaq6oajlbw72ci
Lyndon Words versus Inverse Lyndon Words: Queries on Suffixes and Bordered Words
[chapter]
2020
Lecture Notes in Computer Science
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As a main result, we prove an upper bound on the length of the longest common extension (or longest common prefix) for two factors of a word w. ...
This property suggests that, given two words sharing a common overlap, their Lyndon factorizations could be used to capture the common overlap of these two words. ...
Let w ∈ Σ + be a word which is not an inverse Lyndon word and let ICFL(w) =
A Bound on the Length of the Longest Common Prefix Given a word w and two factors x, y of w, we denote by lcp(x, y) the longest ...
doi:10.1007/978-3-030-40608-0_27
fatcat:q6mrzxpfojecbkd3hzdpaumuae
On the tiling by translation problem
2009
Discrete Applied Mathematics
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By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudo-square polyominoes, improving the previous quadratic ...
algorithm of Gambini and Vuillon. ...
Our algorithms borrow from Lothaire [14] (for instance) that the Longest-Common-Factor, the Longest-Common-Prefix and the Longest-Common-Suffix in two words may be computed in linear time. ...
doi:10.1016/j.dam.2008.05.026
fatcat:cnsbk33devbyloesxwj6acj4su
Construction Of A Rich Word Containing Given Two Factors
[article]
2019
arXiv
pre-print
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It is known that there are pairs of rich words that cannot be factors of a common rich word. ...
A finite word w with w=n contains at most n+1 distinct palindromic factors. If the bound n+1 is attained, the word w is called rich. Let (w) be the set of factors of the word w. ...
The author acknowledges support by the Czech Science Foundation grant GAČR 13-03538S and by the Grant Agency of the Czech Technical University in Prague, grant No. SGS14/205/OHK4/3T/14. ...
arXiv:1904.10202v1
fatcat:jfbt5gtbbnhcdpa4hcl3k4jeou
Finite-Repetition threshold for infinite ternary words
2011
Electronic Proceedings in Theoretical Computer Science
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It is the smallest rational number FRt(a) for which there exists an infinite word whose finite factors have exponent at most FRt(a) and that contains a finite number of factors with exponent r(a). ...
We show that FRt(3)=r(3)=7/4 and that the bound is achieved with an infinite word containing only two 7/4-exponent words, the smallest number. ...
Acknowledgments We warmly thank Pascal Ochem for pointing his powerful result on word morphisms and for profitable discussions. ...
doi:10.4204/eptcs.63.7
fatcat:5bp5n76xwrhgnbculmdb6zghxa
A string-matching interpretation of the equation xmyn = zp
1992
Theoretical Computer Science
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Question: find all maximal factors of \I' which are prefixes of a word of X*. ...
Crochemore, A string-matching interpretation of the equation x"y" = zD, Theoretical Computer Science 92 (1992) 145-164. ...
Let us mention the classical Knuth-Morris-Pratt (KMP) algorithm [12] , generalized in [l] , and an algorithm computing the longest common factor of two words [S] ). ...
doi:10.1016/0304-3975(92)90140-b
fatcat:h6ws46tsdvbi3oznm2qv5o6n3e
Longest (Sub-)Periodic Subsequence
[article]
2022
arXiv
pre-print
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We present an algorithm computing the longest periodic subsequence of a string of length n in O(n^7) time with O(n^4) words of space. ...
We obtain improvements when restricting the exponents or extending the search allowing the reported subsequence to be subperiodic down to O(n^3) time and O(n^2) words of space. ...
[13] generalized this setting to consider the longest such subsequence common of two texts T and S of length n, and gave an algorithm computing this sequence in O(n 6 ) time using O(n 4 ) space, also ...
arXiv:2202.07189v1
fatcat:dz6vawgy6zcmpis5e3iikehk4q
A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino
[article]
2016
arXiv
pre-print
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A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. ...
This improves on the O(n^18)-time algorithm of Keating and Vince and generalizes recent work by Brlek, Provençal, Fédou, and the second author. ...
Acknowledgements The authors wish to thank anonymous reviewers for comments that improved the correctness of the paper. ...
arXiv:1507.02762v2
fatcat:nnkfqm63ajg53ia4v4nzsbf6da
Paper Similarity Detection Method Based on Distance Matrix Model with Row-Column Order Penalty Factor
2014
Journal of Multimedia
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This model integrates the characteristics of vector detection, hamming distance and the longest common substring and carries out detection specific to near-synonyms, word deletion and changes in word order ...
In the aspect of similarity comparison, a distance matrix model with row-column order penalty factor is proposed, which recognizes new words through search engine exponent. ...
Otherwise it is the longest common substring affected by order penalty factor. ...
doi:10.4304/jmm.9.8.998-1004
fatcat:kxwcwivtabbntoaru7adonbfw4
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