Smoothed Complexity Theory

  • Markus Bläser
  • Bodo Manthey
Conference paper

DOI: 10.1007/978-3-642-32589-2_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)
Cite this paper as:
Bläser M., Manthey B. (2012) Smoothed Complexity Theory. In: Rovan B., Sassone V., Widmayer P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg

Abstract

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the inherent difficulty of problems.

Smoothed analysis is a hybrid of worst-case and average-case analysis and compensates some of their drawbacks. Despite its success for the analysis of single algorithms and problems, there is no embedding of smoothed analysis into computational complexity theory, which is necessary to classify problems according to their intrinsic difficulty.

We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first results.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Markus Bläser
    • 1
  • Bodo Manthey
    • 2
  1. 1.Saarland UniversityGermany
  2. 2.University of TwenteThe Netherlands

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