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The complexity of checking consistency of pedigree information and related problems

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Abstract

Consistency checking is a fundamental computational problem in genetics. Given a pedigree and information on the genotypes (of some) of the individuals in it, the aim of consistency checking is to determine whether these data are consistent with the classic Mendelian laws of inheritance. This problem arose originally from the geneticists' need to filter their input data from erroneous information, and is well motivated from both a biological and a sociological viewpoint. This paper shows that consistency checking is NP-complete, even with focus on a single gene and in the presence of three allele. Several other results on the computational complexity of problems from genetics that are related to consistency checking are also offered. In particular, it is shown that checking the consistency of pedigrees over two alleles, and of pedigrees without loops, can be done in polynomial time.

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Authors and Affiliations

  1. Basic Research in Computer Science, Centre of the Danish National Research Foundation, Department of Computer Science, Aalborg University, Fr. Bajersvej 7E, 9220, Aalborg ⇍, Denmark

    Luca Aceto, Jens A. Hansen, Anna Ingólfsdóttir, Jacob Johnsen & John Knudsen

  2. DeCODE Genetics, Sturlagata 8, 101, Reykvavík, Iceland

    Anna Ingólfsdóttir

Authors
  1. Luca Aceto
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  2. Jens A. Hansen
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  3. Anna Ingólfsdóttir
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  4. Jacob Johnsen
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  5. John Knudsen
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Corresponding author

Correspondence to Luca Aceto.

Additional information

Luca Aceto is an associate professor at the Dept. Computer Science, Aalborg University, and is a board member of BRICS. He has previously held various academic positions at the University of Sussex (UK), INRIA-Sophia Antipolis (France), Hewlett-Packard Laboratories (Pisa Science Center, Italy), and BRICS. His main research interests include: semantics of concurrency logic in computer science, applications of equational logic in computer science, structural operational semantics, and computational complexity of verification problems and of problems in bioinformatics.

Anna Ingólfsdóttir is an associate professor at the Department of Computer Science, Aalborg University. She also works as a researcher at deCODE Genetics, and is a board member of BRICS. She has previously held various visiting academic positions at the Univ. Sussex (UK) and the Univ. Florence (Italy). Her research interests include: semantics of concurrency, linkage analysis, bioinformatics, logic in computer science, applications of equational logic in computer science, structural operational semantics, and computational complexity of verification problems and of problems in bioinformatics.

Jens A. Hansen, Jacob Johnsen and John Knudsen hold a Master degree in computer science from Aalborg University.

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Aceto, L., Hansen, J.A., Ingólfsdóttir, A. et al. The complexity of checking consistency of pedigree information and related problems. J. Comput. Sci. & Technol. 19, 42–59 (2004). https://doi.org/10.1007/BF02944784

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  • DOI: https://doi.org/10.1007/BF02944784

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