An improved approximation algorithm for ATSP

We revisit the constant-factor approximation algorithm for the asymmetric traveling salesman problem by Svensson, Tarnawski, and Végh [STOC 2018]. We improve on each part of this algorithm. We avoid the reduction to irreducible instances and thus obtain a simpler and much better reduction to vertebrate pairs. We also show that a slight variant of their algorithm for vertebrate pairs has a much smaller approximation ratio. Overall we improve the approximation ratio from 506 to 22+ε for any ε > 0. This also improves the upper bound on the integrality ratio from 319 to 22.

[1]  Amin Saberi,et al.  An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem , 2010, SODA '10.

[2]  Vera Traub,et al.  The asymmetric traveling salesman path LP has constant integrality ratio , 2019, IPCO.

[3]  Nima Anari,et al.  Effective-Resistance-Reducing Flows, Spectrally Thin Trees, and Asymmetric TSP , 2014, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[4]  Alan M. Frieze,et al.  On the worst-case performance of some algorithms for the asymmetric traveling salesman problem , 1982, Networks.

[5]  László A. Végh,et al.  Constant factor approximation for ATSP with two edge weights , 2015, Mathematical Programming.

[6]  László A. Végh,et al.  Constant factor approximation for ATSP with two edge weights , 2018, Math. Program..

[7]  Ola Svensson,et al.  Approximating ATSP by Relaxing Connectivity , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[8]  Moshe Lewenstein,et al.  Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs , 2005, JACM.

[9]  Mohit Singh,et al.  Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs , 2007, APPROX-RANDOM.

[10]  László A. Végh,et al.  A constant-factor approximation algorithm for the asymmetric traveling salesman problem , 2017, STOC.

[11]  Michel X. Goemans,et al.  On the Integrality Ratio for the Asymmetric Traveling Salesman Problem , 2006, Math. Oper. Res..

[12]  Markus Bläser,et al.  A new approximation algorithm for the asymmetric TSP with triangle inequality , 2003, TALG.