Abstract
We analyze a tour-uncrossing heuristic for the Euclidean Travelling Salesperson Problem, showing that its worst-case approximation ratio is \(\varOmega (n)\) and its average-case approximation ratio is \(\varOmega (\sqrt{n})\) in expectation. We furthermore evaluate the approximation performance of this heuristic numerically on average-case instances, and find that it performs far better than the average-case lower bound suggests. This indicates a shortcoming in the approach we use for our analysis, which is a rather common method in the analysis of local search heuristics.
Supported by NWO grant OCENW.KLEIN.176.
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Manthey, B., van Rhijn, J. (2023). Approximation Ineffectiveness of a Tour-Untangling Heuristic. In: Byrka, J., Wiese, A. (eds) Approximation and Online Algorithms . WAOA 2023. Lecture Notes in Computer Science, vol 14297. Springer, Cham. https://doi.org/10.1007/978-3-031-49815-2_1
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