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A Uniform Theory of Adequate Subgraphs for the Genome Median, Halving, and Aliquoting Problems

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Part of the Lecture Notes in Computer Science book series (LNBI,volume 11488)


One of the key computational problems in comparative genomics is the reconstruction of genomes of ancestral species based on genomes of extant species. Since most dramatic changes in genomic architectures are caused by genome rearrangements, this problem is often posed as minimization of the number of genome rearrangements between extant and ancestral genomes. The basic case of three given genomes is known as the genome median problem. Whole genome duplications (WGDs) represent yet another type of dramatic evolutionary events and inspire the reconstruction of pre-duplicated ancestral genomes, referred to as the genome halving problem. Generalization of WGDs to whole genome multiplication events leads to the genome aliquoting problem.

In the present study, we generalize the adequate subgraphs approach previously proposed for the genome median problem to the genome halving and aliquoting problems. Our study lays a theoretical foundation for practical algorithms for the reconstruction of pre-duplicated ancestral genomes.


  • Genome rearrangement
  • Breakpoint graph
  • Adequate subgraph
  • Whole genome duplication
  • Genome halving
  • Genome aliquoting
  • Genome median

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  • DOI: 10.1007/978-3-030-18174-1_7
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  1. 1.

    Here we view genome P as being transformed and P-edges as changing.

  2. 2.

    The classic formulation of the GMP corresponds to \(n = 3\).

  3. 3.

    This enables us to use transformations of alternating graphs, where intermediate graphs do not have genomic interpretations.


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The work of Maria Atamanova was supported by the Government of the Russian Federation (Grant 08-08) and JetBrains Research.

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Correspondence to Pavel Avdeyev .

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Avdeyev, P., Atamanova, M., Alekseyev, M.A. (2019). A Uniform Theory of Adequate Subgraphs for the Genome Median, Halving, and Aliquoting Problems. In: Holmes, I., Martín-Vide, C., Vega-Rodríguez, M. (eds) Algorithms for Computational Biology. AlCoB 2019. Lecture Notes in Computer Science(), vol 11488. Springer, Cham.

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