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Related Concept Videos

Extended Versions of Green’s Theorem01:27

Extended Versions of Green’s Theorem

Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...
Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

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Routh-Hurwitz Criterion I01:15

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Theorems of Pappus and Guldinus: Problem Solving01:12

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Related Experiment Videos

An improved bound on the Maximum Agreement Subtree problem.

Mike Steel1, László A Székely

  • 1Biomathematics Research Centre, University of Canterbury, New Zealand, M.Steel@math.canterbury.ac.nz.

Applied Mathematics Letters
|February 18, 2010
PubMed
Summary
This summary is machine-generated.

We improved the lower bound for the Maximum Agreement Subtree problem. Two binary trees with n leaves share homeomorphic subtrees of at least c log log n leaves.

Related Experiment Videos

Area of Science:

  • Computer Science
  • Discrete Mathematics
  • Computational Biology

Background:

  • The Maximum Agreement Subtree problem seeks the largest subtree common to two or more given trees.
  • Understanding subtree relationships is crucial in fields like phylogenetics and data clustering.
  • Existing bounds on agreement subtrees are essential for analyzing the complexity of tree comparison algorithms.

Purpose of the Study:

  • To improve the lower bound for the extremal version of the Maximum Agreement Subtree problem.
  • To establish a tighter theoretical bound for the size of common subtrees in binary trees.
  • To advance the understanding of tree similarity and its computational implications.

Main Methods:

  • Focusing on the extremal case of the Maximum Agreement Subtree problem.
  • Proving a new lower bound for the size of homeomorphic subtrees.
  • Utilizing techniques from graph theory and combinatorics on words.

Main Results:

  • We demonstrate that any two binary trees on n leaves share homeomorphic subtrees with at least c log log n leaves.
  • The homeomorphism is restricted to be the identity on the leaves, simplifying the structural comparison.
  • This result improves upon previously known lower bounds in the extremal setting.

Conclusions:

  • The improved lower bound provides a significant advancement in the study of tree similarity.
  • Our findings have implications for the efficiency of algorithms dealing with large collections of trees.
  • This work contributes to the theoretical foundations of comparing hierarchical structures.