New results for the Longest Haplotype Reconstruction problem

The haplotyping problem has emerged in recent years as one of the most relevant problems in Computational Biology. In particular, in the Single Individual Haplotyping (SIH) problem, starting from a matrix of incomplete haplotype fragments, the goal is the reconstruction of the two complete haplotype...

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Vydané v:Discrete Applied Mathematics Ročník 160; číslo 9; s. 1299 - 1310
Hlavný autor: Dondi, Riccardo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.06.2012
Predmet:
Algorithms
Approximation
Approximation complexity
Biology
Computation
Computational biology
Fixed-parameter algorithms
Haplotyping
Mathematical analysis
Mathematical models
Reconstruction
Surface hardness
Haplotyping
Approximation complexity
Fixed-parameter algorithms
Computational biology
ISSN:0166-218X, 1872-6771
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Abstract The haplotyping problem has emerged in recent years as one of the most relevant problems in Computational Biology. In particular, in the Single Individual Haplotyping (SIH) problem, starting from a matrix of incomplete haplotype fragments, the goal is the reconstruction of the two complete haplotypes of an individual. In this paper we consider one of the variants of the Single Individual Haplotyping problem, the Longest Haplotyping Reconstruction (LHR) problem. We prove that the LHR problem is NP-hard even in the restricted case when the input matrix is error-free. Furthermore, we investigate the approximation complexity of the problem, and we show that the problem cannot be approximated within factor 2logδnm for any constant δ<1, unless NP⊆DTIME[2polylognm]. Finally, we exhibit a fixed-parameter algorithm for the LHR problem, where the parameter is the size of the two reconstructed haplotypes.
AbstractList The haplotyping problem has emerged in recent years as one of the most relevant problems in Computational Biology. In particular, in the Single Individual Haplotyping (SIH) problem, starting from a matrix of incomplete haplotype fragments, the goal is the reconstruction of the two complete haplotypes of an individual. In this paper we consider one of the variants of the Single Individual Haplotyping problem, the Longest Haplotyping Reconstruction (LHR) problem. We prove that the LHR problem is NP-hard even in the restricted case when the input matrix is error-free. Furthermore, we investigate the approximation complexity of the problem, and we show that the problem cannot be approximated within factor 2logδnm for any constant δ<1, unless NP⊆DTIME[2polylognm]. Finally, we exhibit a fixed-parameter algorithm for the LHR problem, where the parameter is the size of the two reconstructed haplotypes.
The haplotyping problem has emerged in recent years as one of the most relevant problems in Computational Biology. In particular, in the Single Individual Haplotyping (SIH) problem, starting from a matrix of incomplete haplotype fragments, the goal is the reconstruction of the two complete haplotypes of an individual. In this paper we consider one of the variants of the Single Individual Haplotyping problem, the Longest Haplotyping Reconstruction (LHR) problem. We prove that the LHR problem is NP - hard even in the restricted case when the input matrix is error-free. Furthermore, we investigate the approximation complexity of the problem, and we show that the problem cannot be approximated within factor 2 log delta n m for any constant delta < 1 , unless NP [subE] D T I M E [ 2 p o l y log n m ] . Finally, we exhibit a fixed-parameter algorithm for the LHR problem, where the parameter is the size of the two reconstructed haplotypes.
Author Dondi, Riccardo
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Cites_doi 10.1287/ijoc.1040.0073
10.1145/210332.210337
10.1016/S0304-3975(98)00158-3
10.1007/BF02945456
10.1016/S0166-218X(96)00062-5
10.1007/s00453-007-0029-z
10.1145/278298.278306
10.1137/S009753979223842X
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Keywords Haplotyping
Approximation complexity
Fixed-parameter algorithms
Computational biology
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References Bonizzoni, Della Vedova, Dondi, Li (br000025) 2003; 18
Chen, Zhao, Zhang, Zhu (br000030) 2010
Karger, Motwani, Ramkumar (br000060) 1995; 24
Hein, Jiang, Wang, Zhang (br000050) 1996; 71
Alon, Yuster, Zwick (br000010) 1995; 42
Downey, Fellows (br000040) 1999
Greenberg, Hart, Lancia (br000045) 2004; 16
Niedermeier (br000070) 2006
Alimonti, Kann (br000005) 2000; 237
Arora, Lund, Motwani, Sudan, Szegedy (br000015) 1998; 45
Ausiello, Crescenzi, Gambosi, Kann, Marchetti-Spaccamela, Protasi (br000020) 1999
Cilibrasi, van Iersel, Kelk, Tromp (br000035) 2007; 49
Jiang, Li (br000055) 1995; 24
Lancia, Bafna, Istrail, Lippert, Schwartz (br000065) 2001; vol. 2161
Schaefer (br000075) 1978
Arora (10.1016/j.dam.2011.10.014_br000015) 1998; 45
Chen (10.1016/j.dam.2011.10.014_br000030) 2010
Ausiello (10.1016/j.dam.2011.10.014_br000020) 1999
Hein (10.1016/j.dam.2011.10.014_br000050) 1996; 71
Lancia (10.1016/j.dam.2011.10.014_br000065) 2001; vol. 2161
Niedermeier (10.1016/j.dam.2011.10.014_br000070) 2006
Alimonti (10.1016/j.dam.2011.10.014_br000005) 2000; 237
Greenberg (10.1016/j.dam.2011.10.014_br000045) 2004; 16
Jiang (10.1016/j.dam.2011.10.014_br000055) 1995; 24
Alon (10.1016/j.dam.2011.10.014_br000010) 1995; 42
Schaefer (10.1016/j.dam.2011.10.014_br000075) 1978
Downey (10.1016/j.dam.2011.10.014_br000040) 1999
Cilibrasi (10.1016/j.dam.2011.10.014_br000035) 2007; 49
Bonizzoni (10.1016/j.dam.2011.10.014_br000025) 2003; 18
Karger (10.1016/j.dam.2011.10.014_br000060) 1995; 24
References_xml – volume: 24
  start-page: 1122
  year: 1995
  end-page: 1139
  ident: br000055
  article-title: On the approximation of shortest common supersequences and longest common subsequences
  publication-title: SIAM Journal on Computing
– volume: 49
  start-page: 13
  year: 2007
  end-page: 36
  ident: br000035
  article-title: The complexity of the single individual SNP haplotyping problem
  publication-title: Algorithmica
– year: 1999
  ident: br000020
  article-title: Complexity and Approximation: Combinatorial Optimization Problems and their Approximability Properties
– start-page: 173
  year: 2010
  end-page: 183
  ident: br000030
  article-title: New aspects of haplotype inference from SNP fragments
  publication-title: A Practical Guide to Bioinformatics Analysis
– volume: 237
  start-page: 123
  year: 2000
  end-page: 134
  ident: br000005
  article-title: Some APX-completeness results for cubic graphs
  publication-title: Theoretical Computer Science
– volume: 18
  start-page: 675
  year: 2003
  end-page: 688
  ident: br000025
  article-title: The haplotyping problem: an overview of computational models and solutions
  publication-title: Journal of Computer Science and Technology
– year: 2006
  ident: br000070
  article-title: Invitation to Fixed-Parameter Algorithms
– volume: 42
  start-page: 844
  year: 1995
  end-page: 856
  ident: br000010
  article-title: Color-coding
  publication-title: Journal of the ACM
– start-page: 216
  year: 1978
  end-page: 226
  ident: br000075
  article-title: The complexity of satisfiability problems
  publication-title: Tenth Annual ACM Symposium on Theory of Computing
– volume: vol. 2161
  start-page: 182
  year: 2001
  end-page: 193
  ident: br000065
  article-title: SNPs problems, complexity and algorithms
  publication-title: ESA 2001
– year: 1999
  ident: br000040
  article-title: Parameterized Complexity
– volume: 24
  start-page: 1122
  year: 1995
  end-page: 1139
  ident: br000060
  article-title: On approximating the longest path in a graph
  publication-title: SIAM Journal on Computing
– volume: 16
  start-page: 211
  year: 2004
  end-page: 231
  ident: br000045
  article-title: Opportunities for combinatorial optimization in computational biology
  publication-title: INFORMS Journal on Computing
– volume: 45
  start-page: 501
  year: 1998
  end-page: 555
  ident: br000015
  article-title: Proof verification and the hardness of approximation problems
  publication-title: Journal of the ACM
– volume: 71
  start-page: 153
  year: 1996
  end-page: 169
  ident: br000050
  article-title: On the complexity of comparing evolutionary trees
  publication-title: Discrete Applied Mathematics
– volume: 16
  start-page: 211
  issue: 3
  year: 2004
  ident: 10.1016/j.dam.2011.10.014_br000045
  article-title: Opportunities for combinatorial optimization in computational biology
  publication-title: INFORMS Journal on Computing
  doi: 10.1287/ijoc.1040.0073
– start-page: 216
  year: 1978
  ident: 10.1016/j.dam.2011.10.014_br000075
  article-title: The complexity of satisfiability problems
– volume: 42
  start-page: 844
  issue: 4
  year: 1995
  ident: 10.1016/j.dam.2011.10.014_br000010
  article-title: Color-coding
  publication-title: Journal of the ACM
  doi: 10.1145/210332.210337
– volume: 237
  start-page: 123
  issue: 1–2
  year: 2000
  ident: 10.1016/j.dam.2011.10.014_br000005
  article-title: Some APX-completeness results for cubic graphs
  publication-title: Theoretical Computer Science
  doi: 10.1016/S0304-3975(98)00158-3
– year: 1999
  ident: 10.1016/j.dam.2011.10.014_br000040
– volume: 18
  start-page: 675
  year: 2003
  ident: 10.1016/j.dam.2011.10.014_br000025
  article-title: The haplotyping problem: an overview of computational models and solutions
  publication-title: Journal of Computer Science and Technology
  doi: 10.1007/BF02945456
– year: 1999
  ident: 10.1016/j.dam.2011.10.014_br000020
– volume: 71
  start-page: 153
  year: 1996
  ident: 10.1016/j.dam.2011.10.014_br000050
  article-title: On the complexity of comparing evolutionary trees
  publication-title: Discrete Applied Mathematics
  doi: 10.1016/S0166-218X(96)00062-5
– volume: 24
  start-page: 1122
  year: 1995
  ident: 10.1016/j.dam.2011.10.014_br000060
  article-title: On approximating the longest path in a graph
  publication-title: SIAM Journal on Computing
– start-page: 173
  year: 2010
  ident: 10.1016/j.dam.2011.10.014_br000030
  article-title: New aspects of haplotype inference from SNP fragments
– volume: vol. 2161
  start-page: 182
  year: 2001
  ident: 10.1016/j.dam.2011.10.014_br000065
  article-title: SNPs problems, complexity and algorithms
– year: 2006
  ident: 10.1016/j.dam.2011.10.014_br000070
– volume: 49
  start-page: 13
  issue: 1
  year: 2007
  ident: 10.1016/j.dam.2011.10.014_br000035
  article-title: The complexity of the single individual SNP haplotyping problem
  publication-title: Algorithmica
  doi: 10.1007/s00453-007-0029-z
– volume: 45
  start-page: 501
  issue: 3
  year: 1998
  ident: 10.1016/j.dam.2011.10.014_br000015
  article-title: Proof verification and the hardness of approximation problems
  publication-title: Journal of the ACM
  doi: 10.1145/278298.278306
– volume: 24
  start-page: 1122
  year: 1995
  ident: 10.1016/j.dam.2011.10.014_br000055
  article-title: On the approximation of shortest common supersequences and longest common subsequences
  publication-title: SIAM Journal on Computing
  doi: 10.1137/S009753979223842X
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SubjectTerms Algorithms
Approximation
Approximation complexity
Biology
Computation
Computational biology
Fixed-parameter algorithms
Haplotyping
Mathematical analysis
Mathematical models
Reconstruction
Surface hardness
Title New results for the Longest Haplotype Reconstruction problem
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