Better approximation guarantee for Asymmetric TSP
This work addresses a fundamental combinatorial optimization problem in computer science, providing incremental improvements to approximation algorithms.
The authors tackled the Asymmetric Traveling Salesman Problem (ATSP) by improving the approximation ratio to less than 15, and also enhanced results for unweighted digraphs and tours with specific endpoints, while proving better upper bounds on LP relaxation integrality ratios.
We improve the approximation ratio for the Asymmetric TSP to less than 15. We also obtain improved ratios for the special case of unweighted digraphs and the generalization where we ask for a minimum-cost tour with given (distinct) endpoints. Moreover, we prove better upper bounds on the integrality ratios of the natural LP relaxations.