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  • 1.
    de Vlas, Jorke
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering. Univ Utrecht, Netherlands.
    On the Parameterized Complexity of the Perfect Phylogeny Problem2024In: SOFSEM 2024: THEORY AND PRACTICE OF COMPUTER SCIENCE, SPRINGER INTERNATIONAL PUBLISHING AG , 2024, Vol. 14519, p. 169-182Conference paper (Refereed)
    Abstract [en]

    This paper categorizes the parameterized complexity of the algorithmic problems PERFECT PHYLOGENY and TRIANGULATING COLORED GRAPHS when parameterized by the number of genes and colors, respectively. We show that they are complete for the parameterized complexity class XALP using a reduction from TREE-CHAINED MULTICOLOR INDEPENDENT SET and a proof of membership. We introduce the problem TRIANGULATING MULTICOLORED GRAPHS as a stepping stone and prove XALP-completeness for this problem as well. We also show that, assuming the Exponential Time Hypothesis, there exists no algorithm that solves any of these problems in time f(k)n(o(k)), where n is the input size, k the parameter, and f any computable function.

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