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Leaf Area Index Estimation Using Three Distinct Methods in Pure Deciduous Stands

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Published on: August 29, 2019

Slim Tree-Cut Width.

Robert Ganian¹, Viktoriia Korchemna¹

¹Algorithms and Complexity Group, TU Wien, Vienna, Austria.

|July 29, 2024

Summary

This summary is machine-generated.

Introducing slim tree-cut width, a new graph parameter that bridges structural and algorithmic needs for edge-cut analogues of treewidth. This parameter offers a less restrictive alternative to existing methods.

Keywords:

Graph immersions Structural parameters Tree-cut width

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Area of Science:

Graph Theory
Theoretical Computer Science
Algorithms

Background:

Treewidth is a fundamental graph parameter with broad algorithmic applications.
Existing edge-cut analogues like tree-cut width and edge-cut width have limitations in either structural properties or algorithmic utility.
There is a need for a unified parameter that captures both structural and algorithmic aspects for edge cuts.

Purpose of the Study:

To introduce and analyze a novel graph parameter, "slim tree-cut width", as a potential analogue of treewidth for edge cuts.
To demonstrate that slim tree-cut width satisfies both structural and algorithmic requirements, overcoming limitations of previous parameters.
To provide efficient methods for computing and characterizing slim tree-cut width.

Main Methods:

Modification of tree-cut width by adjusting the threshold for thin nodes in decompositions.
Development of an alternative characterization using spanning-tree decompositions.
Characterization via forbidden immersion relations.
Design of an approximation algorithm for computing the parameter.

Main Results:

Slim tree-cut width is shown to be a valid edge-cut based analogue of treewidth, possessing desirable structural and algorithmic properties.
It is less restrictive than the recently introduced edge-cut width.
An alternative characterization via spanning-tree decompositions is established, simplifying its usability.
Forbidden immersion characterizations and an approximation algorithm are presented.

Conclusions:

Slim tree-cut width successfully integrates the desirable properties of previous parameters, offering a robust alternative.
This new parameter holds significant promise for algorithmic graph theory and related fields.
The findings pave the way for new applications and deeper understanding of graph decomposition techniques.