The traveling salesman problem with precedence constraints is one of the most important problems in operations research. Here, we consider the well-known variant where a linear order on k special vertices is given that has to be preserved in any feasible Hamiltonian cycle. This problem is called Ordered TSP and we consider it on input instances where the edge-cost function satisfies a β-relaxed triangle inequality, i.e., where the length of a direct edge cannot exceed the cost of any detour via a third vertex by more than a factor of β > 1. We design two new polynomial-time approximation algorithms for this problems. The first algorithm essentially improves over the best previously known algorithm for almost all values of k and β < 1.12651. The second algorithm gives a further improvement for 2n ≥ 11k + 7 and
CITATION STYLE
Böckenhauer, H. J., & Steinová, M. (2013). Improved approximations for ordered TSP on near-metric graphs, (Extended Abstract). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7741 LNCS, pp. 157–168). https://doi.org/10.1007/978-3-642-35843-2_15
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