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Computing generalized cophenetic distances under all Lp norms: A near-linear time algorithmic framework.

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We present a new algorithm for computing generalized cophenetic distances efficiently across all Lp norms. This advances large-scale tree comparisons in biology by overcoming previous computational limitations.

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Area of Science:

  • Computational Biology
  • Bioinformatics
  • Algorithmic Science

Background:

  • Cophenetic distance is a key metric for comparing biological trees.
  • Existing methods face computational challenges with large datasets.
  • Previous advancements offered near-linear time complexity but were limited to specific vector norms.

Purpose of the Study:

  • To develop a near-linear time algorithmic framework for generalized cophenetic distances applicable to all Lp norms.
  • To enhance the scalability and versatility of large-scale tree comparison methods.
  • To address the limitations of prior frameworks in handling diverse vector norms.

Main Methods:

  • Developed a novel algorithmic framework for generalized cophenetic distance computation.
  • Extended the framework to support all Lp vector norms.
  • Conducted scalability studies to evaluate practical performance.
  • Analyzed the distribution of distance components across various norms.

Main Results:

  • Achieved near-linear time complexity for generalized cophenetic distances across all Lp norms.
  • Demonstrated practical performance and scalability of the new framework.
  • Provided insights into the behavior of generalized cophenetic distances under different vector norms.

Conclusions:

  • The new framework significantly enhances the applicability of generalized cophenetic distances in large-scale biological studies.
  • This work overcomes previous limitations, enabling broader use of these metrics with diverse vector norms.
  • The findings facilitate more versatile and efficient comparative analyses of large biological datasets.