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RECOMB International Workshop on Comparative Genomics

RECOMB-CG 2017: Comparative Genomics pp 156–178Cite as

A Unified ILP Framework for Genome Median, Halving, and Aliquoting Problems Under DCJ

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Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 10562))

Abstract

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 provide polynomial-size integer linear programming formulations for the aforementioned problems. We further obtain such formulations for the restricted versions of the median and halving problems, which have been recently introduced for improving biological relevance.

P. Avdeyevand and N. Alexeev are contributed equally to this work.

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Notes

  1. 1.

    The strand of a gene is typically encoded by a sign. When the strands are ignored, the genomes are represented as permutations of (unsigned) genes.

  2. 2.

    Here we view genome P as evolving and P-edges as changing.

  3. 3.

    Note that V is determined by the genes present in the genomes \(P_1, P_2, \dots , P_q\), and thus V does not depend on the choice of M.

  4. 4.

    Under the inequality \(|a - b| \le c\), we understand a pair of linear inequalities \(a - b \le c\) and \(b - a \le c\).

  5. 5.

    In fact, they also define a genome \(X\in D_m(R)\) and a labeling of gene copies of A and X such that c(A, X) is maximized.

  6. 6.

    In fact, beside R they also define a genome \(X\in D_m(R)\) and a labeling of gene copies of A and X such that \(c(A,X)+c(R,B)\) is maximized.

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Acknowledgements

The work of PA and MAA is supported by the National Science Foundation under the grant No. IIS-1462107. The work of NA and YR is partially supported by the National Science Foundation under the grant No. DMS-1406984.

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Authors and Affiliations

  1. The George Washington University, Washington, D.C., USA

    Pavel Avdeyev, Nikita Alexeev, Yongwu Rong & Max A. Alekseyev

Authors
  1. Pavel Avdeyev
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  2. Nikita Alexeev
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  3. Yongwu Rong
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  4. Max A. Alekseyev
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Correspondence to Pavel Avdeyev .

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Editors and Affiliations

  1. University of Campinas, Campinas, São Paulo, Brazil

    Joao Meidanis

  2. Rice University, Houston, Texas, USA

    Luay Nakhleh

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Avdeyev, P., Alexeev, N., Rong, Y., Alekseyev, M.A. (2017). A Unified ILP Framework for Genome Median, Halving, and Aliquoting Problems Under DCJ. In: Meidanis, J., Nakhleh, L. (eds) Comparative Genomics. RECOMB-CG 2017. Lecture Notes in Computer Science(), vol 10562. Springer, Cham. https://doi.org/10.1007/978-3-319-67979-2_9

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  • DOI: https://doi.org/10.1007/978-3-319-67979-2_9

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