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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
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.
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.
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