Differential Approximation Results for the Traveling Salesman Problem with Distances 1 and 2

Authors:
Jérôme Monnot;Vangelis Th. Paschos;Sophie Toulouse
Affiliations:
-;-;-
Venue:
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Year:
2001

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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 Ɛ 0, it is NP-hard to approximate both problems within better than 5379/5380 + Ɛ.