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Approaching the One-Sided Exemplar Adjacency Number Problem.

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    This study introduces a new method for analyzing genome rearrangements, improving upon the NP-hard Exemplar Adjacency Number problem. The developed algorithm offers a more stable and scalable solution for computing exemplar similarity in large genomes.

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    Area of Science:

    • Computational Biology
    • Bioinformatics
    • Genomics

    Background:

    • The one-sided Exemplar Adjacency Number (EAN) problem aims to maximize common adjacencies between a generic genome and an exemplar genome, but is NP-hard and difficult to approximate.
    • Existing methods struggle with large or unsigned genomes, limiting their practical application in comparative genomics.

    Purpose of the Study:

    • To address the limitations of the EAN problem by introducing a relaxed version, One-sided EAN+, allowing for pseudo-exemplar genomes.
    • To develop a more stable and scalable algorithm for computing exemplar similarity, outperforming existing software.

    Main Methods:

    • Relaxed the EAN problem to One-sided EAN+ by allowing sub-permutations (pseudo-exemplar genomes) of a minimum length k.
    • Formulated the relaxed problem as a maximum independent set on a colored interval graph, proving it remains NP-complete but is fixed-parameter tractable (FPT).
    • Employed integer linear programming (ILP) to ensure each gene appears at most once in the pseudo-exemplar genome and implemented the algorithm for comparison.

    Main Results:

    • The new relaxation is NP-complete but allows for a factor-2 approximation algorithm and is proven to be fixed-parameter tractable (FPT).
    • The implemented algorithm demonstrates superior stability and scalability compared to the GREDU software, successfully processing signed genomes up to 12,000 genes.
    • The algorithm can handle both signed and unsigned genomes, unlike GREDU which falters on large signed genomes and cannot process unsigned ones.

    Conclusions:

    • The One-sided EAN+ problem offers a flexible and computationally tractable approach to genome rearrangement analysis.
    • The developed algorithm provides a significant advancement in efficiently and accurately computing exemplar similarity for large-scale genomic datasets.
    • This work enhances the toolkit for comparative genomics, particularly for analyzing gene duplications and complex genome structures.