A constant-factor approximation algorithm for the asymmetric traveling salesman problem

Series
ACO Colloquium
Time
Thursday, September 21, 2017 - 1:30pm for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Laszlo Vegh – London School of Economics – L.Vegh@lse.ac.uk
Organizer
Prasad Tetali
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation.Our techniques build upon the constant-factor approximation algorithm for the special case of node-weighted metrics. Specifically, we give a generic reduction to structured instances that resemble but are more general than those arising from node-weighted metrics. For those instances, we then solve Local-Connectivity ATSP, a problem known to be equivalent (in terms of constant-factor approximation) to the asymmetric traveling salesman problem.This is joint work with Ola Svensson and Jakub Tarnawski.