Joint ORIE Colloquium - CS Theory Seminar: Laci Vegh (London School of Economics) - A Constant-Factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem

Tuesday, August 29, 2017 at 4:15pm

Frank H. T. Rhodes Hall, 253

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 (EPFL).

 

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