Abstract
The 2-opt heuristic is a very simple local search heuristic for the traveling salesman problem. While it usually converges quickly in practice, its running-time can be exponential in the worst case.
In order to explain the performance of 2-opt, Englert, Röglin, and Vöcking (Algorithmica, to appear) provided a smoothed analysis in the so-called one-step model on d-dimensional Euclidean instances. However, translating their results to the classical model of smoothed analysis, where points are perturbed by Gaussian distributions with standard deviation σ, yields a bound that is only polynomial in n and 1/σ d.
We prove bounds that are polynomial in n and 1/σ for the smoothed running-time with Gaussian perturbations. In particular our analysis for Euclidean distances is much simpler than the existing smoothed analysis.
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Manthey, B., Veenstra, R. (2013). Smoothed Analysis of the 2-Opt Heuristic for the TSP: Polynomial Bounds for Gaussian Noise. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_54
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DOI: https://doi.org/10.1007/978-3-642-45030-3_54
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