Cut-Equivalent Trees are Optimal for Min-Cut Queries

Explore a 24-minute IEEE conference talk on cut-equivalent trees and their optimality for min-cut queries. Delve into previous algorithms for constructing Gomory-Hu trees, min-cut data structures, and the equivalence between min-cut data structures and cut-equivalent trees. Learn about the Gomory-Hu algorithm description, tournament expansion, and the challenges of designing fast approximation algorithms. Gain insights from speakers Amir Abboud, Robert Krauthgamer, and Ohad Trabelsi as they discuss their findings and present approximation ideas for this complex graph theory topic.

Introduction
Previous Algorithms for constructing GH Trees
Min-Cut Data-Structure
Equivalence Between Min-Cut Data Structure and Cut-Equivalent Tree
First Result:Yes!
Corollaries
Gomory-Hu Algorithm Description
Tournament
Expansion
Gomory-Hu Fails Using Approx.
Issues with Designing Fast Approx. Algorithms
Approximation Idea