Smoothed Analysis of the 2-Opt Heuristic for the TSP: Polynomial Bounds for Gaussian Noise

  • Bodo Manthey
  • Rianne Veenstra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bodo Manthey
    • 1
  • Rianne Veenstra
    • 1
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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