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

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.

Английский

STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on the Theory of Computing, June 25–29, 2018 in Los Angeles. – New York : Association for Computing Machinery, 2018. – P. 204–213.