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Linear Time Additively Exact Algorithm for Transformation of Chain-Cycle Graphs for Arbitrary Costs of Deletions and Insertions

Author

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  • Konstantin Gorbunov

    (Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoi Karetnyi, 19, Moscow 127994, Russia)

  • Vassily Lyubetsky

    (Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoi Karetnyi, 19, Moscow 127994, Russia)

Abstract

We propose a novel linear time algorithm which, given any directed weighted graphs a and b with vertex degrees 1 or 2, constructs a sequence of operations transforming a into b . The total cost of operations in this sequence is minimal among all possible ones or differs from the minimum by an additive constant that depends only on operation costs but not on the graphs themselves; this difference is small as compared to the operation costs and is explicitly computed. We assume that the double cut and join operations have identical costs, and costs of the deletion and insertion operations are arbitrary strictly positive rational numbers.

Suggested Citation

  • Konstantin Gorbunov & Vassily Lyubetsky, 2020. "Linear Time Additively Exact Algorithm for Transformation of Chain-Cycle Graphs for Arbitrary Costs of Deletions and Insertions," Mathematics, MDPI, vol. 8(11), pages 1-30, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2001-:d:442596
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    References listed on IDEAS

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    1. Nicholas H. Putnam & Thomas Butts & David E. K. Ferrier & Rebecca F. Furlong & Uffe Hellsten & Takeshi Kawashima & Marc Robinson-Rechavi & Eiichi Shoguchi & Astrid Terry & Jr-Kai Yu & E`lia Benito-Gut, 2008. "The amphioxus genome and the evolution of the chordate karyotype," Nature, Nature, vol. 453(7198), pages 1064-1071, June.
    2. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
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    Cited by:

    1. Konstantin Gorbunov & Vassily Lyubetsky, 2024. "Algorithms for the Reconstruction of Genomic Structures with Proofs of Their Low Polynomial Complexity and High Exactness," Mathematics, MDPI, vol. 12(6), pages 1-26, March.
    2. Konstantin Gorbunov & Vassily Lyubetsky, 2023. "Constructing an Evolutionary Tree and Path–Cycle Graph Evolution along It," Mathematics, MDPI, vol. 11(9), pages 1-39, April.

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