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##
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The consensus string problem and the complexity of comparing hidden Markov models

2002
*
Journal of computer and system sciences (Print)
*

In this paper we consider

doi:10.1016/s0022-0000(02)00009-0
fatcat:oz3a7nthw5ey3l2p26kgfpzmqm
*the**problem**of*computing*the*most likely*string*, or*consensus**string*, generated by a given model, and its implications*on**the*complexity*of*comparing hidden Markov models. ... We show that computing*the**consensus**string*, and approximating its probability within any constant factor, is NP-*hard*, and that*the*same holds for*the*closely related labeling*problem*for class hidden ... Finally, we would like to express our gratitude to an anonymous referee for bringing our attention to*the*labeling*problem*, pointing out that our*hardness*results could easily be extended to this*problem*...##
###
The consensus string problem for a metric is NP-complete

2003
*
Journal of Discrete Algorithms
*

In this paper, we show that

doi:10.1016/s1570-8667(03)00011-x
fatcat:xjjal6dvvvgxxe6ooh4aevrsq4
*the**problem**of*finding a*consensus**string*based*on**consensus*error is NP-complete when*the*penalty matrix is a metric. ... Given a set S*of**strings*, a*consensus**string**of*S based*on**consensus*error is a*string*w that minimizes*the*sum*of**the*distances between w and all*the**strings*in S. ...*The**consensus**string**problem*with*consensus*error (resp. with radius) is to find a*consensus**string*based*on**consensus*error (resp. based*on*radius). ...##
###
On The Parameterized Intractability Of Motif Search Problems*

2006
*
Combinatorica
*

We show that Closest Substring,

doi:10.1007/s00493-006-0011-4
fatcat:ouh6uhre2fgednkk3lidu4bawq
*one**of**the*most important*problems*in*the*field*of**consensus**string*analysis, is W[1]-*hard*when parameterized by*the*number k*of*input*strings*(and remains so, even over ... Our W[1]-*hardness*result for Closest Substring generalizes to*Consensus*Patterns, a*problem*arising in computational biology. ... Our Main Results Our main results are negative*ones*: we show that Closest Substring and*Consensus*Patterns are W[1]-*hard*with respect to*the*parameter k*of**the*number*of*input*strings*, even in case*of*...##
###
Finding Optimal Alignment and Consensus of Circular Strings
[chapter]

2010
*
Lecture Notes in Computer Science
*

*The*

*consensus*

*string*

*problem*is finding a representative

*string*(

*consensus*)

*of*a given set

*of*

*strings*, and it has been studied

*on*linear

*strings*extensively. ... We consider

*the*

*problem*

*of*finding

*the*optimal alignment and

*consensus*(

*string*)

*of*circular

*strings*. ... We can find a

*string*that minimizes

*the*distance sum by selecting

*the*symbol occurring most often in each position

*of*

*the*

*strings*in S. However,

*Problem*CR is

*hard*in general. ...

##
###
Consensus Optimizing Both Distance Sum and Radius
[chapter]

2009
*
Lecture Notes in Computer Science
*

*The*

*consensus*

*string*

*problem*is finding a representative

*string*(

*consensus*)

*of*a given set S

*of*

*strings*. ... In this paper we deal with

*the*

*consensus*

*string*

*problems*optimizing both distance sum and radius, where

*the*distance sum is

*the*sum

*of*(Hamming) distances from

*the*

*strings*in S to

*the*

*consensus*and

*the*...

*The*

*consensus*

*string*

*problem*is finding a representative

*string*(

*consensus*)

*of*a given set S

*of*

*strings*. ...

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

2017
*
arXiv
*
pre-print

We consider

arXiv:1702.08238v1
fatcat:sgfkepwjnbcergfxsdxzleehsu
*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*. ... We prove that this*problem*is W[1]-*hard*when parameterized by*the*maximum length*of*input*strings*. ...*The*instance I*of**Consensus*Patterns contains N occurrences*of**strings*V i , i ∈ [n], and*one*occurrence*of**strings*E j , j ∈ [m].*The*target length is m = k + 1. ...##
###
Parameterized Intractability of Motif Search Problems
[article]

2002
*
arXiv
*
pre-print

We show that Closest Substring,

arXiv:cs/0205056v1
fatcat:nqfc4bsucvdqfdw2tolxlsx4p4
*one**of**the*most important*problems*in*the*field*of*biological sequence analysis, is W[1]-*hard*when parameterized by*the*number k*of*input*strings*(and remains so, even over ... Our W[1]-*hardness*result for Closest Substring generalizes to*Consensus*Patterns, a*problem**of*similar significance in computational biology. ... Unfortunately, our main results are negative*ones*: we show that Closest Substring and*Consensus*Patterns are W[1]-*hard*with respect to*the*parameter k*of**the*number*of*input*strings*, even in case*of*a ...##
###
Outlier Detection for DNA Fragment Assembly
[article]

2011
*
arXiv
*
pre-print

Given n length-ℓ

arXiv:1111.0376v2
fatcat:wbu4olvawbbb7ch667ku55vs6e
*strings*S ={s_1, ..., s_n} over a constant size alphabet Σ together with parameters d and k,*the*objective in*the**Consensus**String*with Outliers*problem*is to find a subset S^**of*S*of*... Specifically, when k is allowed to be arbitrary*the**Consensus**String*with Outliers*problem*does not admit an EPTAS unless FPT=W[1]. This*hardness*result holds even for binary alphabets. 3. ... Approximating*Consensus**String*with Outliers We prove*the*existence*of*a PTAS for*the*Min-distance*Consensus**String*with Outliers*problem*. Our algorithm is based*on*random sampling. ...##
###
Multivariate Algorithmics for NP-Hard String Problems

2014
*
Bulletin of the European Association for Theoretical Computer Science
*

This motivates

dblp:journals/eatcs/BulteauHKN14
fatcat:g3gh2kna2je23mwxoa7uqn4iq4
*the*search for (fixed-parameter) tractable special cases*of*these*problems*. ...*String**problems*arise in various applications ranging from text mining to biological sequence analysis. Many*string**problems*are NP-*hard*. ... We thank Henning Fernau (Universität Trier) and Stéphane Vialette (Université Paris-Est Marne-la-Vallé) for reading a previous draft*of**the*manuscript and providing us with their constructive feedback. ...##
###
Consensus Strings with Small Maximum Distance and Small Distance Sum

2018
*
International Symposium on Mathematical Foundations of Computer Science
*

*The*parameterised complexity

*of*

*consensus*

*string*

*problems*(Closest

*String*, Closest Substring, Closest

*String*with Outliers) is investigated in a more general setting, i. e., with a bound

*on*

*the*maximum ... from

*the*literature regarding

*the*classical

*problem*variants with only

*one*distance bound. ...

*The*

*consensus*

*string*

*problems*are a formalisation

*of*this computational task and most variants

*of*them are NP-

*hard*. ...

##
###
Consensus Patterns (Probably) Has no EPTAS
[chapter]

2015
*
Lecture Notes in Computer Science
*

To

doi:10.1007/978-3-662-48350-3_21
fatcat:rxcfl7a3brafzg36wddek7gh2y
*the*best*of*our knowledge,*Consensus*Patterns is*the*first*problem*that admits a PTAS, and is fixed parameter tractable when parameterized by*the*value*of**the*objective function but does not admit an ... Given n length-L*strings*S = {s 1 , . . . , s n } over a constant size alphabet Σ together with an integer , where ≤ L,*the*objective*of**Consensus*Patterns is to find a length-*string*s, a substring t i ... Our result rules out*the*possibility*of*a (1+ ) approximation algorithms with running time f (1/ )n O(1) , while*the*best PTAS for*Consensus*Patterns has running time n O(1/ 4 ) . ...##
###
On the hardness of maximum rank aggregation problems

2015
*
Journal of Discrete Algorithms
*

*The*rank aggregation

*problem*consists in finding a

*consensus*ranking

*on*a set

*of*alternatives, based

*on*

*the*preferences

*of*individual voters. ... We provide a general schema via local permutations for

*the*NP-

*hardness*

*of*

*the*maximum rank aggregation

*problems*under all distances which satisfy some general requirements. ... These requirements are met by our collection

*of*distances. We associate

*the*maximum rank aggregations

*on*permutations and

*the*

*string*

*consensus*

*problem*

*on*

*strings*. ...

##
###
Subject Index

2003
*
Journal of Discrete Algorithms
*

*The*

*consensus*

*string*

*problem*for a metric is NP- complete, 111 NP-

*hardness*

*The*non-approximability

*of*bicriteria network de- sign

*problems*, 339 Odd perfect number

*On*

*the*number

*of*distinct prime ...

*Consensus*

*problem*

*Consensus*in Byzantine asynchronous systems, 185

*Consensus*

*string*

*The*

*consensus*

*string*

*problem*for a metric is NP- complete, 111 Crossdating Applying an edit distance to

*the*matching ...

##
###
The most probable string: an algorithmic study

2013
*
Journal of Logic and Computation
*

We also study a randomized algorithm solving

doi:10.1093/logcom/exs049
fatcat:p7x6yi43qrgkroxnjmjbur4fmu
*the*same*problem*. Finally, we report links between*the*length*of**the**consensus**string*and*the*probability*of*this*string*. ...*The**problem**of*finding*the**consensus*(most probable*string*) for a distribution generated by a weighted finite automaton or a probabilistic grammar is related to a number*of*important questions: computing ... This work was supported in part by*the*IST Programme*of**the*European Community, under*the*Pascal 2 Network*of*Excellence, IST-2007-216886. ...##
###
A Uniform Framework for Ordered Restriction Map Problems

1998
*
Journal of Computational Biology
*

We achieve this by identifying

doi:10.1089/cmb.1998.5.725
pmid:10072087
fatcat:nyalco65hvf6fg3iwm5zhvfnky
*the*following approaches to*the*ordered restriction map*problem*: (1) using data*consensus*or agreement, and, (2) optimizing a characteristic function*of**the*data. ... However, it is not a priori clear as to how these cost functions relate to*one*another and to*the*underlying*problem*. ... Acknowledgements I would like to thank Bud Mishra and Thomas Ananthraman for their careful reading*of**the*paper and their comments. ...
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