Abstract
We propose an algorithm which returns a single Hamiltonian cycle with performance guarantee on both objectives. The algorithm is analysed in three cases. When both (resp. at least one) objective function(s) fulfill(s) the triangle inequality, the approximation ratio is \(\frac{5}{12}-\varepsilon\approx 0.41\) (resp. \(\frac{3}{8}-\varepsilon\)). When the triangle inequality is not assumed on any objective function, the algorithm is \(\frac{1+2\sqrt{2}}{14} -\varepsilon\approx 0.27\)-approximate.
This research has been supported by the project ANR-09-BLAN-0361 GUaranteed Efficiency for PAReto optimal solutions Determination (GUEPARD).
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Bazgan, C., Gourvès, L., Monnot, J., Pascual, F. (2012). Single Approximation for Biobjective Max TSP. In: Solis-Oba, R., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol 7164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29116-6_5
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