A Slightly Improved Approximation Algorithm for Metric TSP

Explore an improved approximation algorithm for the Metric Traveling Salesman Problem in this 46-minute lecture by Nathan Klein from the University of Washington. Delve into Christofides' Algorithm, 2-uniform spanning trees, and concentration properties. Learn about feasible solutions, small perturbations, and cuts of interest. Examine the dream of induction, example hierarchies, and increasing slack. Discover how probabilistic tools are applied in the analysis and consider future directions for polynomial geometers in solving this classic optimization problem.

Intro
Metric TSP
Christofides' Algorithm
Approximation algorithms
Background #2: 2-uniform spanning trees
Algorithm we study
Why 2-uniform trees may help
Concentration property
A feasible solution
Applying a small perturbation
Cuts of interest
Stars have no even near min cuts
Degree cut case
Dream of induction
Example hierarchy
Increasing slack
Overall approach
Using probabilistic tool #1
Using probabilistic tool #2
Analysis
Next steps for polynomial geometers