Abstract
We prove that both minimum and maximum traveling salesman problems on complete graphs with edge-distances 1 and 2 are approximable within 3/4. Based upon this result, we improve the standard approximation ratio known for maximum traveling salesman with distances 1 and 2 from 3/4 to 7/8. Finally, we prove that, for any ϵ > 0, it is NP-hard to approximate both problems within better than 5379/5380 + ϵ.
Cite
CITATION STYLE
Monnot, J., Paschos, V. T., & Toulouse, S. (2001). Differential approximation results for the traveling salesman problem with distances 1 and 2. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2138, pp. 275–286). Springer Verlag. https://doi.org/10.1007/3-540-44669-9_27
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