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Improved Approximations for Hard Optimization Problems via Problem Instance Classification

  • Hans-Joachim Böckenhauer
  • Juraj Hromkovič
  • Tobias Mömke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6570)

Abstract

Under the usual complexity-theoretic assumptions like \(\mathcal{P}\neq\mathcal{NP}\), many practically relevant optimization problems are provably hard to solve or even to approximate. But most of these hardness results are derived for worst-case scenarios, and it is in many cases not clear whether the actual problem instances arising in practical applications exhibit this worst-case behaviour. Thus, a recent branch of algorithmic research aims at a more fine-grained analysis of the hardness of optimization problems. The main idea behind this analysis is to find some parameter according to which one can classify the hardness of problem instances. This approach does not only lead to new hardness results, but can also be used to design improved approximation algorithms for practically relevant subclasses of problem instances.

In this paper, we survey several different approaches for such improved approximation results achieved by a fine-grained classification of problem instances.

Keywords

Span Tree Problem Instance Approximation Ratio Travel Salesman Problem Travel Salesman Problem 
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 2011

Authors and Affiliations

  • Hans-Joachim Böckenhauer
    • 1
  • Juraj Hromkovič
    • 1
  • Tobias Mömke
    • 1
  1. 1.Department of Computer ScienceETH ZurichSwitzerland

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