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In this paper, we study the genomic median of 3 problem with respect to the rank distance, which looks for a genome that minimizes the sum of the rank distances to three given genomes. We advance the knowledge on the mathematical properties of this problem, and settle its computational complexity, showing it is NP-hard. We also prove that the gap between exact and relaxed solutions of the problem can be arbitrarily large.

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Time Complexity and Relaxation Gap for the Rank Median of Three Genomes

  • 会议论文

  • 发表日期：

    2026年

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  • Victor de Moraes,
  • Joao Meidanis

摘要

In this paper, we study the genomic median of 3 problem with respect to the rank distance, which looks for a genome that minimizes the sum of the rank distances to three given genomes. We advance the knowledge on the mathematical properties of this problem, and settle its computational complexity, showing it is NP-hard. We also prove that the gap between exact and relaxed solutions of the problem can be arbitrarily large.