Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
Journal of Discrete Algorithms
On the relationship between ATSP and the cycle cover problem
Theoretical Computer Science
On Approximating Restricted Cycle Covers
SIAM Journal on Computing
Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
An improved approximation algorithm for the ATSP with parameterized triangle inequality
Journal of Algorithms
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Improved approximation algorithms for metric max TSP
ESA'05 Proceedings of the 13th annual European conference on Algorithms
35/44-Approximation for asymmetric maximum TSP with triangle inequality
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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In this paper, we study the asymmetric traveling salesman problem (ATSP) with strengthened triangle inequality, i.e. for some $\gamma\in [\frac{1}{2},1)$ the edge weights satisfy w (u ,v ) ≤ γ (w (u ,x ) + w (x ,v )) for all distinct vertices u ,v ,x . We present two approximation algorithms for this problem. The first one is very simple and has approximation ratio $\frac{1}{2(1-\gamma)}$, which is better than all previous results for all $\gamma \in (\frac{1}{2},1)$. The second algorithm is more involved but it also gives a much better approximation ratio: $\frac{2-\gamma}{3(1-\gamma)}+O(\frac{1}{n})$ when γ γ 0 , and $\frac{1}{2}(1+\gamma)^2 + \epsilon$ for any ε 0 when γ ≤ γ 0 , where γ 0 ≅ 0.7003.