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The Distance Formula01:20

The Distance Formula

In geometry, measuring the direct distance between two points on a plane is essential in various practical and theoretical applications. Whether in navigation, engineering, or computer graphics, determining the shortest path between two locations involves using the distance formula. This formula is derived from the Pythagorean Theorem, which relates the lengths of the sides of a right triangle. On a coordinate plane, the horizontal and vertical distances between two points serve as the legs of...
Phylogenetic Trees03:21

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Phylogenetic trees come in many forms. It matters in which sequence the organisms are arranged from the bottom to the top of the tree, but the branches can rotate at their nodes without altering the information. The lines connecting individual nodes can be straight, angled, or even curved.The length of the branches can depict time or the relative amount of change among organisms. For instance, the branch length might indicate the number of amino acid changes in the sequence that underlies the...
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Related Experiment Video

Updated: Jun 1, 2026

Tree Core Analysis with X-ray Computed Tomography
06:56

Tree Core Analysis with X-ray Computed Tomography

Published on: September 22, 2023

A sub-cubic time algorithm for computing the quartet distance between two general trees.

Jesper Nielsen1, Anders K Kristensen, Thomas Mailund

  • 1Bioinformatics Research Centre (BiRC), Aarhus University, C, F, Møllers Alle 8, DK-8000 Aarhus C, Denmark. jn@birc.au.dk.

Algorithms for Molecular Biology : AMB
|June 7, 2011
PubMed
Summary
This summary is machine-generated.

A new algorithm efficiently computes the quartet distance between phylogenetic trees. This method is faster than existing approaches for comparing evolutionary relationships, aiding in phylogenetic inference accuracy.

More Related Videos

A Practical Guide to Phylogenetics for Nonexperts
12:00

A Practical Guide to Phylogenetics for Nonexperts

Published on: February 5, 2014

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Last Updated: Jun 1, 2026

Tree Core Analysis with X-ray Computed Tomography
06:56

Tree Core Analysis with X-ray Computed Tomography

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A Practical Guide to Phylogenetics for Nonexperts
12:00

A Practical Guide to Phylogenetics for Nonexperts

Published on: February 5, 2014

Area of Science:

  • Computational Biology
  • Phylogenetics
  • Evolutionary Biology

Background:

  • Phylogenetic tree inference algorithms can produce varying tree topologies.
  • Quantifying differences between trees is crucial for understanding algorithm effects.
  • Quartet distance measures topological differences by counting differing quartet arrangements.

Purpose of the Study:

  • To develop a novel algorithm for calculating the quartet distance between general phylogenetic trees.
  • To improve the efficiency of comparing tree structures in phylogenetic analysis.

Main Methods:

  • Developed a new algorithm for computing quartet distance.
  • Algorithm complexity is sub-cubic in the number of leaves.
  • Algorithm performance is independent of the degree of inner nodes in the trees.

Main Results:

  • The new algorithm achieves sub-cubic time and space complexity for general trees.
  • This represents the fastest known algorithm for quartet distance computation in general trees.
  • The algorithm's performance is independent of node degree.

Conclusions:

  • The implemented algorithm significantly outperforms competing methods.
  • Empirical results suggest near-quadratic time complexity in practice.
  • The new algorithm offers a substantial speed improvement for phylogenetic tree comparison.