A Constant-Factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem

演讲人: Ola Svensson the theory group at the School of Computer and Communication Sciences, EPFL
时间: 2023-07-14 16:10-2023-07-14 18:00
地点:FIT 1-315 or Tencent Meeting ID: 981-127-091

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). 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.

The main idea of our approach is a reduction to Subtour Partition Cover, an easier problem obtained by significantly relaxing the general connectivity requirements into local connectivity conditions. We first show that any algorithm for Subtour Partition Cover can be turned into an algorithm for ATSP while only losing a small constant factor in the performance guarantee. Next, we present a reduction from general ATSP instances to structured instances, on which we then solve Subtour Partition Cover, yielding our constant-factor approximation algorithm for ATSP.


Ola Svensson is an Associate Professor active in the theory group at the School of Computer and Communication Sciences, EPFL. His research interests include approximation algorithms, combinatorial optimization, computational complexity and scheduling. He received the best papers awards at FOCS 2011, FOCS 2017 and STOC 2018.