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

Laurent Bulteau, Christian Komusiewicz
2013 arXiv   pre-print
We present the first fixed-parameter algorithm for 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.  ... 
arXiv:1305.0649v2 fatcat:b5hqhyoyhjau3henkqn6kxewdi

Minimum Common String Partition Parameterized by Partition Size Is Fixed-Parameter Tractable [chapter]

Laurent Bulteau, Christian Komusiewicz
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
We present the first fixed-parameter algorithm for 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.  ... 
doi:10.1137/1.9781611973402.8 dblp:conf/soda/BulteauK14 fatcat:faimivr5qnbs3abpf7iary6oxu

Minimum Common String Partition Parameterized [chapter]

Peter Damaschke
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".  ... 
doi:10.1007/978-3-540-87361-7_8 fatcat:qv56zo6a2fakbjhsc57yvlayom

Minimum common string partition revisited

Haitao Jiang, Binhai Zhu, Daming Zhu, Hong Zhu
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.  ... 
doi:10.1007/s10878-010-9370-2 fatcat:2eqp7fzjhrd4pexqc4cusetlkm

Minimum Common String Partition Revisited [chapter]

Haitao Jiang, Binhai Zhu, Daming Zhu, Hong Zhu
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.  ... 
doi:10.1007/978-3-642-14553-7_7 fatcat:nyeaojyymrdf3icc7vlex5frca

Parameterized Algorithms in Bioinformatics: An Overview

Laurent Bulteau, Mathias Weller
2019 Algorithms  
This work surveys recent developments of 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.  ... 
doi:10.3390/a12120256 fatcat:4dhjdnpibzh43iifgan2fu6bwa

A general approach to uniformly handle different string metrics based on heterogeneous alphabets

Francesco Cauteruccio, Alessandro Cucchiarelli, Christian Morbidoni, Giorgio Terracina, Domenico Ursino
2020 IEEE Access  
INDEX TERMS 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.  ... 
doi:10.1109/access.2020.2978893 fatcat:wzla6foeivg7nki6gave3bimeu

Synergies between Adaptive Analysis of Algorithms, Parameterized Complexity, Compressed Data Structures and Compressed Indices (Dagstuhl Seminar 18281)

Jérémy Barbay, Johannes Fischer, Stefan Kratsch, Srinivasa Rao Satti, Michael Wagner
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, 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?  ... 
doi:10.4230/dagrep.8.7.44 dblp:journals/dagstuhl-reports/BarbayFKS18 fatcat:ygmzm5oc6zefphnrfmq4h6tpnu

Sparse Dynamic Programming for Longest Common Subsequence from Fragments

Brenda S. Baker, Raffaele Giancarlo
2002 Journal of Algorithms  
: given a pair of 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.  ... 
doi:10.1006/jagm.2002.1214 fatcat:ukz7ji6tfrbcbhxx2dswx2peq4

Consensus Patterns parameterized by input string length is W[1]-hard [article]

Laurent Bulteau
2017 arXiv   pre-print
We prove that this problem is W[1]-hard when 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 ∈  ... 
arXiv:1702.08238v1 fatcat:sgfkepwjnbcergfxsdxzleehsu

Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)

Magnus Bordewich, Britta Dorn, Simone Linz, Rolf Niedermeier, Michael Wagner
2020 Dagstuhl Reports  
The closest related results are an FPT algorithm for Closest 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.  ... 
doi:10.4230/dagrep.9.10.134 dblp:journals/dagstuhl-reports/BordewichDLN19 fatcat:nypkd3nzjvg5jdsd3cidktwyei

Parameterized Tractability of the Maximum-Duo Preservation String Mapping Problem [article]

Stefano Beretta, Mauro Castelli, Riccardo Dondi
2015 arXiv   pre-print
In this paper we investigate the 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.  ... 
arXiv:1512.03220v1 fatcat:ddxcvyqchrerlnil5ms2icubvm

Subject Index

2007 Journal of Discrete Algorithms  
load coloring problem, 533 Graph 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  ... 
doi:10.1016/s1570-8667(07)00076-7 fatcat:wfqxglrznfb6do3wyittd5pfbi

Solving the Minimum Common String Partition Problem with the Help of Ants [article]

S.M. Ferdous, M. Sohel Rahman
2014 arXiv   pre-print
In this paper, we consider the problem of finding a 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.  ... 
arXiv:1401.4539v2 fatcat:l4ghxtrcp5bn5dhtcryipezgxm

Fixed-Parameter Algorithms for Scaffold Filling [chapter]

Laurent Bulteau, Anna Paola Carrieri, Riccardo Dondi
2014 Lecture Notes in Computer Science  
While both problems are known to be NP-hard, their 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] .  ... 
doi:10.1007/978-3-319-09174-7_12 fatcat:bawk2a6m2rdbhemtdz7jglmqfy
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