Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, November 18, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Marvin Künnemann (Max Planck Institute for Informatics)

On the Smoothed Approximation Performance of the 2-OPT heuristic

The 2-OPT heuristic is a very simple and popular approach to solve Euclidean TSP: given a tour on the input points, we iteratively replace pairs of edges by swapping their endpoints as long as this creates a shorter tour. Despite its popularity, our theoretical understanding of the practical performance of this approach is still quite restricted. As a welcome exception, a smoothed analysis proved useful to justify the heuristic's fast running time observed in practice (Englert, Röglin, Vöcking 2007).

In this talk, we focus on the question of how well the smoothed analysis paradigm also explains the practical approximation performance of the 2-OPT heuristic. We analyze the heuristic when the input points are slightly perturbed by random Gaussian noise and present new upper and lower bounds on the approximation ratio that depend on the magnitude of the perturbation.

This is joint work with Bodo Manthey (University of Twente, The Netherlands).

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