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Longest Lyndon Substring After Edit

Yuki Urabe, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Marc Herbstritt
2018 Annual Symposium on Combinatorial Pattern Matching  
After O(n) time and space preprocessing, our algorithm returns LLS(T ) in O(log n) time for any single character edit.  ...  After O(n) time and space preprocessing, our algorithm returns LLS(T ) in O(l log σ + log n) time for any block edit where σ is the number of distinct characters in T .  ...  The goal there was to compute, given strings S and T , the longest common factor of strings S and T where T is a string which is obtained by a single character edit operation on T .  ... 
doi:10.4230/lipics.cpm.2018.19 dblp:conf/cpm/UrabeNIBT18 fatcat:rikiejsrnfegrn55jajxxab2pu

Longest Common Substring Made Fully Dynamic

Amihood Amir, Panagiotis Charalampopoulos, Solon P. Pissis, Jakub Radoszewski, Michael Wagner
2019 European Symposium on Algorithms  
Given two strings S and T , each of length at most n, the longest common substring (LCS) problem is to find a longest substring common to S and T .  ...  In the fully dynamic setting, edit operations are allowed in either of the two strings, and the problem is to find an LCS after each edit.  ...  Introduction Given two strings S and T , each of length at most n, the longest common substring (LCS) problem, also known as the longest common factor problem, is to find a longest substring common to  ... 
doi:10.4230/lipics.esa.2019.6 dblp:conf/esa/AmirCPR19 fatcat:vhha5ndeu5dyrkohazx5t43wmy

Dynamic and Internal Longest Common Substring

Amihood Amir, Panagiotis Charalampopoulos, Solon P. Pissis, Jakub Radoszewski
2020 Algorithmica  
., and Urabe et al.) studied analogously restricted dynamic variants of problems on strings; specifically, computing the longest palindrome and the Lyndon factorization of a string after a single edit  ...  Given two strings S and T, each of length at most n, the longest common substring (LCS) problem is to find a longest substring common to S and T.  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1007/s00453-020-00744-0 fatcat:jqzu2ou4tvc4na72tdnriuhzom

Longest Common Substring Made Fully Dynamic [article]

Amihood Amir, Panagiotis Charalampopoulos, Solon P. Pissis, Jakub Radoszewski
2018 arXiv   pre-print
In particular, we show how to return an LCS in Õ(n^2/3) time (or Õ(√(n)) time if edits are allowed in only one of the two strings) after each operation using Õ(n) space.  ...  In the fully dynamic version of the problem, edit operations are allowed in either of the two strings, and we are asked to report an LCS after each such operation.  ...  Introduction Longest Common Substring (LCS) Problem In the longest common substring (LCS) problem, also known as longest common factor problem, we are given two strings S and T , each of length at most  ... 
arXiv:1804.08731v2 fatcat:6uzghlv55zbptnt7mrr4rhk7da

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  
Notably, we show that our technique can be extended to the edit distance model with the same time and space complexities.  ...  Specifically, our algorithms run in O(n log k n log log n) time on average using O(n) space.  ...  The edit distance between x and y is the minimum total cost of a sequence of edit operations (insertions, deletions, substitutions) required to transform x into y.  ... 
doi:10.1007/978-3-030-00479-8_3 fatcat:2xhap3e2xfaihggp3p4ai365fa

Avoiding approximate repetitions with respect to the longest common subsequence distance

Serina Camungol, Narad Rampersad
2016 Involve. A Journal of Mathematics  
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.  ...  In their work, they measured the similarity of x and x' using either the Hamming distance or the edit distance.  ...  The most common metrics used to measure the distance between strings are the edit distance, the Hamming distance, and the longest common subsequence metric.  ... 
doi:10.2140/involve.2016.9.657 fatcat:mnfsqn3wkzaidh2xtryxhx2dpy

Longest substring palindrome after edit

Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Marc Herbstritt
2018 Annual Symposium on Combinatorial Pattern Matching  
In this paper, we consider the problem of finding the LSPal after the string is edited.  ...  It is known that the length of the longest substring palindromes (LSPals) of a given string T of length n can be computed in O(n) time by Manacher's algorithm [J. ACM '75].  ...  operation on T .  ... 
doi:10.4230/lipics.cpm.2018.12 dblp:conf/cpm/FunakoshiNIBT18 fatcat:goydlmhzk5hm7mawyvdvsynv3q

Longest Alignment with Edits in Data Streams [article]

Elena Grigorescu, Erfan Sadeqi Azer, Samson Zhou
2017 arXiv   pre-print
We study the problem of identifying a longest substring of S and T that forms a d-near-alignment under the edit distance, in the simultaneous streaming model.  ...  We give several algorithms, including an exact one-pass algorithm that uses O(d^2+d n) bits of space. We couple these results with comparable lower bounds.  ...  It is also related to the Longest Common Subsequence problem, in which the goal is to find the longest common subsequence of S and T .  ... 
arXiv:1711.04367v1 fatcat:mmqpwmjtb5cy3nc5wxdj3jjzjy

Faster Queries for Longest Substring Palindrome After Block Edit

Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Michael Wagner
2019 Annual Symposium on Combinatorial Pattern Matching  
We can preprocess T in O(n) time and space such that later, we can answer in O(log min{σ, log n}) time the longest substring palindrome after a single character edit operation (insertion, deletion, or  ...  In this paper, we consider the problem of finding the LSPal after the string is edited.  ...  [1] proposed an algorithm to find the longest common factor (LCF ) of two strings, after a single character edit operation is performed in one of the strings.  ... 
doi:10.4230/lipics.cpm.2019.27 dblp:conf/cpm/FunakoshiNIBT19 fatcat:6ojz4dt5q5gelczyamhz66cqhu

A Survey on Longest Common Subsequence

Deena Nath
2018 International Journal for Research in Applied Science and Engineering Technology  
This paper is a survey which briefly describes the successful attempts made to get the longest common subsequence of two strings.  ...  The main aim of this paper is to present a general observation of popular longest common subsequence algorithms and study their functions in multiple applications.  ...  Some Related Works 1) The string editing problem is as attempt of transforming edit operation to minimise the cost.  ... 
doi:10.22214/ijraset.2018.4746 fatcat:b4e2dygazrccpaahekz6caczuq

Edit distance with move operations

Dana Shapira, James A. Storer
2007 Journal of Discrete Algorithms  
The traditional edit-distance problem is to find the minimum number of insert-character and delete-character (and sometimes change character) operations required to transform one string into another.  ...  Although a greedy algorithm is known to have poor (a polynomial factor) worst case performance, we present a polynomial time greedy algorithm for non-recursive moves which on a subclass of instances of  ...  Acknowledgements We thank Maxime Crochemore for suggesting the edit distance with the exchange operation, which helped to motivate this work.  ... 
doi:10.1016/j.jda.2005.01.010 fatcat:qjxzs63kvfhkrnpkr2lovh3seu

Edit Distance with Move Operations [chapter]

Dana Shapira, James A. Storer
2002 Lecture Notes in Computer Science  
The traditional edit-distance problem is to find the minimum number of insert-character and delete-character (and sometimes change character) operations required to transform one string into another.  ...  Although a greedy algorithm is known to have poor (a polynomial factor) worst case performance, we present a polynomial time greedy algorithm for non-recursive moves which on a sub class of instances of  ...  Acknowledgments We thank Maxime Crochemore for suggesting the edit distance with the exchange operation, which helped to motivate this work.  ... 
doi:10.1007/3-540-45452-7_9 fatcat:mxbsmtdazbd53axrj6emobqfkq

Efficient algorithms for the block edit problems

Hsing-Yen Ann, Chang-Biau Yang, Yung-Hsing Peng, Bern-Cherng Liaw
2010 Information and Computation  
In this paper, we focus on the edit distance between two given strings where block-edit operations are allowed and better fitting to the human natural edit behaviors.  ...  Then we show that with some preprocessing, the minimum block edit distances of these three problems can be obtained by dynamic programming in O(nm), O(nm log m) and O(nm 2 ) time, respectively, where n  ...  This internal node is the lowest common ancestor (LCA) of Y R j and some X R h , and our aim is to get the longest common prefix (LCP) LCP Y R j , X R h .  ... 
doi:10.1016/j.ic.2009.12.001 fatcat:5fethilqnfcunf2kf67ghrzifq

Edit Distance with Block Operations

Michal Ganczorz, Pawel Gawrychowski, Artur Jez, Tomasz Kociumaka, Michael Wagner
2018 European Symposium on Algorithms  
The edit distance with block moves is equivalent, up to a constant factor, to the common string partition problem, in which we are given two strings s, t and the goal is to partition s into minimal number  ...  We consider the problem of edit distance in which block operations are allowed, i.e. we ask for the minimal number of (block) operations that are needed to transform a string s to t.  ...  It is folklore knowledge that edit distance with move operations corresponds to a common partition; more precisely, it is within constant factor of the minimal common partition.  ... 
doi:10.4230/lipics.esa.2018.33 dblp:conf/esa/GanczorzGJK18 fatcat:kgeonzxmgfc7bfj6vxusxv5hc4

A Modification of the Landau-Vishkin Algorithm Computing Longest Common Extensions via Suffix Arrays [chapter]

Rodrigo de Castro Miranda, Mauricio Ayala-Rincón
2005 Lecture Notes in Computer Science  
Suffix trees are used for preprocessing the sequences allowing an O(1) running time computation of the longest common extensions between substrings.  ...  We present a variation of the Landau-Vishkin algorithm which instead of suffix trees uses suffix arrays for computing the longest common extensions, thereby improving actual space usage.  ...  We have shown that it is possible to change the Landau-Vishkin approximate string matching algorithm to use enhanced suffix arrays instead of suffix trees for its computation of longest common extensions  ... 
doi:10.1007/11532323_25 fatcat:dyplnkcednbohfqttzzdwmqfe4
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