A Quantization Framework for Smoothed Analysis of Euclidean Optimization Problems

  • Radu Curticapean
  • Marvin Künnemann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)


We consider the smoothed analysis of Euclidean optimization problems. Here, input points are sampled according to density functions that are bounded by a sufficiently small smoothness parameter φ. For such inputs, we provide a general and systematic approach that allows to design linear-time approximation algorithms whose output is asymptotically optimal, both in expectation and with high probability.

Applications of our framework include maximum matching, maximum TSP, and the classical problems of k-means clustering and bin packing. Apart from generalizing corresponding average-case analyses, our results extend and simplify a polynomial-time probable approximation scheme on multidimensional bin packing on φ-smooth instances, where φ is constant (Karger and Onak, SODA 2007).

Both techniques and applications of our rounding-based approach are orthogonal to the only other framework for smoothed analysis on Euclidean problems we are aware of (Bläser et al., Algorithmica 2012).


Approximation Scheme Approximation Ratio Maximum Match Quantization Framework Polynomial Approximation Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Radu Curticapean
    • 1
  • Marvin Künnemann
    • 1
    • 2
  1. 1.Universität des SaarlandesSaarbrückenGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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