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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

Description:

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.

A Slightly Improved Approximation Algorithm for Metric TSP

Simons Institute

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#Computer Science #Algorithms and Data Structures #Travelling Salesman Problem (TSP) #Algorithms #Approximation Algorithms