The traveling salesman problem with distances one and two
Mathematics of Operations Research
P-Complete Approximation Problems
Journal of the ACM (JACM)
A new approximation algorithm for the asymmetric TSP with triangle inequality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On Approximating Restricted Cycle Covers
SIAM Journal on Computing
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation results for the weighted P4 partition problem
Journal of Discrete Algorithms
On the integrality gap of the subtour LP for the 1,2-TSP
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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The minimum traveling salesman problem with distances one and two is the following problem: Given a complete undirected graph G=(V,E) with a cost function w: E→ {1, 2}, find a Hamiltonian tour of minimum cost. In this paper, we provide an approximation algorithm for this problem achieving a performance guarantee of $\frac{315}{271}$. This algorithm can be further improved obtaining a performance guarantee of $\frac{65}{56}$. This is better than the one achieved by Papadimitriou and Yannakakis [8], with a ratio $\frac{7}{6}$, more than a decade ago. We enhance their algorithm by an involved procedure and find an improved lower bound for the cost of an optimal Hamiltonian tour.