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

Rune B. Lyngsø, Christian N.S. Pedersen
2002 Journal of computer and system sciences (Print)  
In this paper we consider 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  ... 
doi:10.1016/s0022-0000(02)00009-0 fatcat:oz3a7nthw5ey3l2p26kgfpzmqm

The consensus string problem for a metric is NP-complete

Jeong Seop Sim, Kunsoo Park
2003 Journal of Discrete Algorithms  
In this paper, we show that 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).  ... 
doi:10.1016/s1570-8667(03)00011-x fatcat:xjjal6dvvvgxxe6ooh4aevrsq4

On The Parameterized Intractability Of Motif Search Problems*

Michael R. Fellows, Jens Gramm†, Rolf Niedermeier‡
2006 Combinatorica  
We show that Closest Substring, 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  ... 
doi:10.1007/s00493-006-0011-4 fatcat:ouh6uhre2fgednkk3lidu4bawq

Finding Optimal Alignment and Consensus of Circular Strings [chapter]

Taehyung Lee, Joong Chae Na, Heejin Park, Kunsoo Park, Jeong Seop Sim
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.  ... 
doi:10.1007/978-3-642-13509-5_28 fatcat:mxwhkae6p5aypnon47egsshnfm

Consensus Optimizing Both Distance Sum and Radius [chapter]

Amihood Amir, Gad M. Landau, Joong Chae Na, Heejin Park, Kunsoo Park, Jeong Seop Sim
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.  ... 
doi:10.1007/978-3-642-03784-9_23 fatcat:63vvkavaqrdjvk4penv2nce5oi

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

Laurent Bulteau
2017 arXiv   pre-print
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.  ...  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.  ... 
arXiv:1702.08238v1 fatcat:sgfkepwjnbcergfxsdxzleehsu

Parameterized Intractability of Motif Search Problems [article]

Michael R. Fellows, Jens Gramm, Rolf Niedermeier
2002 arXiv   pre-print
We show that Closest Substring, 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  ... 
arXiv:cs/0205056v1 fatcat:nqfc4bsucvdqfdw2tolxlsx4p4

Outlier Detection for DNA Fragment Assembly [article]

Christina Boucher and Christine Lo and Daniel Lokshtanov
2011 arXiv   pre-print
Given n length-ℓ 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.  ... 
arXiv:1111.0376v2 fatcat:wbu4olvawbbb7ch667ku55vs6e

Multivariate Algorithmics for NP-Hard String Problems

Laurent Bulteau, Falk Hüffner, Christian Komusiewicz, Rolf Niedermeier
2014 Bulletin of the European Association for Theoretical Computer Science  
This motivates 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.  ... 
dblp:journals/eatcs/BulteauHKN14 fatcat:g3gh2kna2je23mwxoa7uqn4iq4

Consensus Strings with Small Maximum Distance and Small Distance Sum

Laurent Bulteau, Markus L. Schmid, Michael Wagner
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.  ... 
doi:10.4230/lipics.mfcs.2018.1 dblp:conf/mfcs/BulteauS18 fatcat:ocmal4ziubgfnamkzgtz4ft7eq

Consensus Patterns (Probably) Has no EPTAS [chapter]

Christina Boucher, Christine Lo, Daniel Lokshantov
2015 Lecture Notes in Computer Science  
To 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 ) .  ... 
doi:10.1007/978-3-662-48350-3_21 fatcat:rxcfl7a3brafzg36wddek7gh2y

On the hardness of maximum rank aggregation problems

Christian Bachmaier, Franz J. Brandenburg, Andreas Gleißner, Andreas Hofmeier
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.  ... 
doi:10.1016/j.jda.2014.10.002 fatcat:7m5fh6hfi5fytibmcn2y4klfoa

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  ... 
doi:10.1016/s1570-8667(03)00075-3 fatcat:icg7if3uingibmjwy2mjud4rwe

The most probable string: an algorithmic study

C. de la Higuera, J. Oncina
2013 Journal of Logic and Computation  
We also study a randomized algorithm solving 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.  ... 
doi:10.1093/logcom/exs049 fatcat:p7x6yi43qrgkroxnjmjbur4fmu

A Uniform Framework for Ordered Restriction Map Problems

LAXMI PARIDA
1998 Journal of Computational Biology  
We achieve this by identifying 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.  ... 
doi:10.1089/cmb.1998.5.725 pmid:10072087 fatcat:nyalco65hvf6fg3iwm5zhvfnky
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