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Minimum Common String Partition Parameterized by Partition Size is Fixed-Parameter Tractable
[article]

2013
*
arXiv
*
pre-print

We present the first fixed-parameter algorithm for

arXiv:1305.0649v2
fatcat:b5hqhyoyhjau3henkqn6kxewdi
*Minimum**Common**String**Partition*using only parameter k. ... The NP-hard*Minimum**Common**String**Partition*problem asks whether two*strings*x and y can each be*partitioned*into at most k substrings, called blocks, such that both*partitions*use exactly the same blocks ... We study the problem of finding a*minimum*-size CSP:*Minimum**Common**String**Partition*(MCSP) Input: Two*strings*x and y of length n, and an integer k. ...##
###
Minimum Common String Partition Parameterized by Partition Size Is Fixed-Parameter Tractable
[chapter]

2013
*
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We present the first fixed-parameter algorithm for

doi:10.1137/1.9781611973402.8
dblp:conf/soda/BulteauK14
fatcat:faimivr5qnbs3abpf7iary6oxu
*Minimum**Common**String**Partition*using only parameter k. ... The NP-hard*Minimum**Common**String**Partition*problem asks whether two*strings*x and y can each be*partitioned*into at most k substrings such that both*partitions*use exactly the same substrings in a different ...*Minimum**Common**String**Partition*can be solved in k 21k 2 poly(n) time; it is thus fixed-parameter tractable with respect to the*partition*size k. Proof. ...##
###
Minimum Common String Partition Parameterized
[chapter]

*
Lecture Notes in Computer Science
*

*Minimum*

*Common*

*String*

*Partition*(MCSP) and related problems are of interest in, e.g., comparative genomics, DNA fingerprint assembly, and ortholog assignment. ... Given two

*strings*with equal symbol content, the problem is to

*partition*one

*string*into k blocks, k as small as possible, and to permute them so as to obtain the other

*string*. ... The algorithm has a simple structure: First we roughly guess the breaks and the matching of blocks "in

*parameterized*time". ...

##
###
Minimum common string partition revisited

2010
*
Journal of combinatorial optimization
*

*Minimum*

*Common*

*String*

*Partition*(MCSP) has drawn much attention due to its application in genome rearrangement. ... , k is the number of blocks in the optimal

*common*

*partition*and x is a constant integer. ... The

*minimum*

*common*

*string*

*partition*problem is to compute a

*common*

*partition*of X and Y with the

*minimum*number of blocks. ...

##
###
Minimum Common String Partition Revisited
[chapter]

2010
*
Lecture Notes in Computer Science
*

*Minimum*

*Common*

*String*

*Partition*(MCSP) has drawn much attention due to its application in genome rearrangement. ... , k is the number of blocks in the optimal

*common*

*partition*and x is a constant integer. ... The

*minimum*

*common*

*string*

*partition*problem is to compute a

*common*

*partition*of X and Y with the

*minimum*number of blocks. ...

##
###
Parameterized Algorithms in Bioinformatics: An Overview

2019
*
Algorithms
*

This work surveys recent developments of

doi:10.3390/a12120256
fatcat:4dhjdnpibzh43iifgan2fu6bwa
*parameterized*algorithms and complexity for important NP-hard problems in bioinformatics. ... Figure 3 . 3 A*minimum**common**string**partition*for the*strings*abcdabcaed and daedbcabca. ... Intuitively, most genes from the genomes of two close species should have a simple*common**string**partition*.*Minimum**Common**String**Partition*Problem Description. ...##
###
A general approach to uniformly handle different string metrics based on heterogeneous alphabets

2020
*
IEEE Access
*

INDEX TERMS

doi:10.1109/access.2020.2978893
fatcat:wzla6foeivg7nki6gave3bimeu
*String*metrics, generalized*string*similarity framework, edit distance, Jaccard distance. ... In the last few years, we have assisted in a great increase of the usage of*strings*in the most disparate areas. ... The longest*parameterized**common*subsequence has been studied also in [38] , where a quite different notion of*parameterized**string*is adopted. ...##
###
Synergies between Adaptive Analysis of Algorithms, Parameterized Complexity, Compressed Data Structures and Compressed Indices (Dagstuhl Seminar 18281)

2019
*
Dagstuhl Reports
*

From the 8th of July 2018 to the 13th of July 2018, a Dagstuhl Seminar took place with the topic "Synergies between Adaptive Analysis of Algorithms,

doi:10.4230/dagrep.8.7.44
dblp:journals/dagstuhl-reports/BarbayFKS18
fatcat:ygmzm5oc6zefphnrfmq4h6tpnu
*Parameterized*Complexity, Compressed Data Structures ... is Clique*Partition*, where given a graph G = (V, E) one aims to*partition*G into a*minimum*number of cliques. ... Can polynomial*parameterized*algorithm be used in practice to*partition*optimally practical graphs? ...##
###
Sparse Dynamic Programming for Longest Common Subsequence from Fragments

2002
*
Journal of Algorithms
*

: given a pair of

doi:10.1006/jagm.2002.1214
fatcat:ukz7ji6tfrbcbhxx2dswx2peq4
*strings*X and Y (of length n and m, respectively) and a set M of matching substrings of X and Y , find the longest*common*subsequence based only on the symbol correspondences induced ... We provide a new sparse dynamic programming technique that extends the Hunt-Szymanski paradigm for the computation of the longest*common*subsequence (LCS) and apply it to solve the LCS from Fragments problem ... CONCLUDING REMARKS We have shown how to compute longest*common*subsequence of two*strings*X and Y from Fragments, i.e., from a set of "matching" pairs of substrings of the two input*strings*. ...##
###
Consensus Patterns parameterized by input string length is W[1]-hard
[article]

2017
*
arXiv
*
pre-print

We prove that this problem is W[1]-hard when

arXiv:1702.08238v1
fatcat:sgfkepwjnbcergfxsdxzleehsu
*parameterized*by the maximum length of input*strings*. ... We consider the Consensus Patterns problem, where, given a set of input*strings*, one is asked to extract a long-enough pattern which appears (with some errors) in all*strings*. ... The Consensus Patterns of {V i | i ∈ [n]} (i.e., the*strings*of length k + 1 at*minimum*total distance from*strings*V i ) are the*strings*of the form S = $v 1,i1 . . . v k,i k with i 1 , . . . , i k ∈ ...##
###
Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)

2020
*
Dagstuhl Reports
*

The closest related results are an FPT algorithm for Closest

doi:10.4230/dagrep.9.10.134
dblp:journals/dagstuhl-reports/BordewichDLN19
fatcat:nypkd3nzjvg5jdsd3cidktwyei
*String**parameterized*by the distance (allowing substitutions only) and FPT algorithm for LCS*parameterized*by the distance plus number of*strings*... one seeks a*common*pattern appearing in a (possibly large) set of (possibly long)*strings*. ...##
###
Parameterized Tractability of the Maximum-Duo Preservation String Mapping Problem
[article]

2015
*
arXiv
*
pre-print

In this paper we investigate the

arXiv:1512.03220v1
fatcat:ddxcvyqchrerlnil5ms2icubvm
*parameterized*complexity of the Maximum-Duo Preservation*String*Mapping Problem, the complementary of the*Minimum**Common**String**Partition*Problem. ... We show that this problem is fixed-parameter tractable when*parameterized*by the number k of conserved duos, by first giving a*parameterized*algorithm based on the color-coding technique and then presenting ... However, the fixedparameter algorithms we propose can be of interests for describing the whole*parameterized*complexity status of the*Minimum**Common**String**Partition*Problem and its variants. ...##
###
Subject Index

2007
*
Journal of Discrete Algorithms
*

load coloring problem,
533
Graph

doi:10.1016/s1570-8667(07)00076-7
fatcat:wfqxglrznfb6do3wyittd5pfbi
*partitioning*On the*minimum*load coloring problem, 533 Graph theory Cut problems in graphs with a budget constraint, 262 Grid graph Maximum integer multiflow and ... repeat problem, 243; An upper bound on the hardness of exact matrix based motif discovery, 706*String*matching*Parameterized*matching with mismatches, 135 Student-optimal Two algorithms for the Student-Project ...##
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Solving the Minimum Common String Partition Problem with the Help of Ants
[article]

2014
*
arXiv
*
pre-print

In this paper, we consider the problem of finding a

arXiv:1401.4539v2
fatcat:l4ghxtrcp5bn5dhtcryipezgxm
*minimum**common**partition*of two*strings*. The problem has its application in genome comparison. ... The*minimum**common**string**partition*problem is to find a*common**partition*of X, Y with the*minimum*number of blocks. ... For example, if (X, Y ) = {"ababcab","abcabab"}, then one of the*minimum**common**partition*sets is π ={"ab","abc","ab"} and the*minimum**common**partition*size is 3. ...##
###
Fixed-Parameter Algorithms for Scaffold Filling
[chapter]

2014
*
Lecture Notes in Computer Science
*

While both problems are known to be NP-hard, their

doi:10.1007/978-3-319-09174-7_12
fatcat:bawk2a6m2rdbhemtdz7jglmqfy
*parameterized*complexity when*parameterized*by the number of*common*adjacencies of the resulting genomes is still open. ... the first problem, called One-sided scaffold filling, we are given an incomplete genome B and a complete genome A, and we look for the insertion of missing genes into B with the goal of maximizing the*common*... However, the*parameterized*complexity of the One/Twosided scaffold filling problems, when*parameterized*only by the maximum number of*common*adjacencies k, has been left open in [12] . ...
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