Smoothed Analysis: Analysis of Algorithms Beyond Worst Case

Bodo Manthey and Heiko Röglin 1
  • 1  University of Bonn, Department of Computer Science, Bonn, Deutschland


Many algorithms perform very well in practice, but have a poor worst-case performance. The reason for this discrepancy is that worst-case analysis is often a way too pessimistic measure for the performance of an algorithm. In order to provide a more realistic performance measure that can explain the practical performance of algorithms, smoothed analysis has been introduced. It is a hybrid of the classical worst-case analysis and average-case analysis, where the performance on inputs is measured that are subject to random noise. We give a gentle, not too formal introduction to smoothed analysis by means of two examples: the k-means method for clustering and the Nemhauser/Ullmann algorithm for the knapsack problem.

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it - Information Technology is a strictly peer-reviewed scientific journal. It is the oldest German journal in the field of information technology. Today, the major aim of it - Information Technology is highlighting issues on ongoing newsworthy areas in information technology and informatics and their application. It aims at presenting the topics with a holistic view.