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    Area of Science:

    • Computational Biology
    • Bioinformatics
    • Phylogenetics

    Background:

    • The split-row problem (SR) is vital for perfect phylogeny reconstruction from mixed tumor samples.
    • SR involves minimizing operations to transform a binary matrix into one representing a perfect phylogeny.
    • The problem has been proven to be NP-hard.

    Purpose of the Study:

    • To develop an efficient kernelization algorithm for the split-row problem.
    • To reduce the input size for exact algorithms solving SR.
    • To improve the computational efficiency of phylogenetic reconstruction from tumor data.

    Main Methods:

    • Introduced a kernelization algorithm for the split-row problem.
    • Derived bounds for the kernel size: at most 3ϵ(M) rows and 4ϵ(M) - 1 columns.
    • Analyzed the time complexity of the kernelization algorithm as $O(\text{max}(m^{0.373}n^2, mn^{1.373}))$.

    Main Results:

    • Demonstrated that the split-row problem admits a polynomial-size kernel.
    • The kernel size is bounded by a function of the minimum cost ϵ(M).
    • The kernelization algorithm provides a significant speedup for small values of ϵ(M).

    Conclusions:

    • The developed kernelization algorithm effectively preprocesses instances of the split-row problem.
    • This preprocessing can substantially accelerate existing exact algorithms for SR.
    • The findings contribute to more efficient computational methods in phylogenetics and cancer research.