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Modeling the Functional Network for Spatial Navigation in the Human Brain

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Better-than- -approximations for leaf-to-leaf tree and connectivity augmentation.

Federica Cecchetto¹, Vera Traub², Rico Zenklusen¹

¹Department of Mathematics, ETH Zurich, Zurich, Switzerland.

Mathematical Programming

|August 12, 2024

Summary

This summary is machine-generated.

We developed a simple matching-based method for network design problems, specifically the leaf-to-leaf Connectivity Augmentation Problem (CAP). This new approach achieves a better approximation factor, improving upon existing techniques for CAP and TAP instances.

Keywords:

Approximation algorithms Combinatorial optimization Connectivity augmentation Tree augmentation

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Area of Science:

Computer Science
Operations Research
Algorithm Design

Background:

The Connectivity Augmentation Problem (CAP) and Tree Augmentation Problem (TAP) are fundamental network design challenges.
Recent research focuses on approximation algorithms with factors below 2, with the current best at 1.393.

Purpose of the Study:

To present a novel, simple matching-based method for leaf-to-leaf instances of CAP.
To improve approximation factors for specific CAP and TAP problem classes.

Main Methods:

A new matching-based algorithm for leaf-to-leaf CAP instances.
Combining the new method with existing techniques and a stack analysis approach.

Main Results:

Achieved a -approximation for Leaf-to-Leaf CAP by selecting the better of the new solution and an existing one.
Improved the approximation factor to 1.29 for a nontrivial class of TAP/CAP instances, surpassing the threshold.

Conclusions:

The new matching-based method offers a simpler approach to CAP and TAP.
The improved approximation factor of 1.29 represents a significant advancement for specific network design problems.