We consider the approximability of the TSP problem in graphs that satisfy a relaxed form of triangle inequality. More precisely, we assume that for some parameter τ ≥ 1, the distances satisfy the inequality dist(x,y) ≤τ. (dist(x,z)+ dist(z,y)) for every triple of vertices x, y, and z. We obtain a 4τ approximation and also show that for some ∈ > 0 it is NP-hard to obtain a (1 + ∈τ) approximation. Our upper bound improves upon the earlier known ratio of (3τ 2/2/+τ/2)[1] for all values of τ > 7/3.
CITATION STYLE
Bender, M. A., & Chekuri, C. (1999). Performance guarantees for the TSP with a parameterized triangle inequality. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1663, pp. 80–85). Springer Verlag. https://doi.org/10.1007/3-540-48447-7_10
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