On LP-Relaxations for the Tree Augmentation Problem

Explore a lecture on LP-relaxations for the tree augmentation problem, delivered by Zeev Nutov at the Hausdorff Center for Mathematics. Delve into the intricacies of the Tree Augmentation Problem, its equivalent formulations, and the significance of studying it. Examine the Cut-LP and dual-fitting algorithms, and understand the concept of shadow-minimal solutions along with their properties. Investigate twin-links, stems, and blocking trees, and learn about an LP and its dual, including initial assignment of duals. The lecture, part of the Hausdorff Trimester Program on Combinatorial Optimization, also covers additional possible constraints and presents an algorithm for solving the problem. Gain insights into this complex topic through a comprehensive 33-minute presentation that combines theoretical concepts with practical applications in the field of combinatorial optimization.

The Tree Augmentation Problem
Equivalent Formulation 2
Why is it interesting?
The Cut-LP
Dual-fitting algorithms
Shadow-minimal solutions
Properties of shadow minimal solutions
Twin-links and stems
Blocking trees
An LP and its dual
Initial assignment of duals
The algorithm
Additional possible constraints