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Methods and Applications of Informatics and Information Technology

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Smoothed Analysis: Analysis of Algorithms Beyond Worst Case

Bodo Manthey / Heiko Röglin
  • 1 University of Bonn, Department of Computer Science, Bonn, Deutschland
Published Online: 2011-12-01 | DOI: https://doi.org/10.1524/itit.2011.0654

Abstract

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.

Zusammenfassung

Viele Algorithmen sind in der Praxis effizient, obwohl ihre Laufzeit im Worst Case sehr schlecht ist. Der Grund für diese Diskrepanz ist, dass die reine Betrachtung des Worst Case oft ein viel zu pessimistisches Maß darstellt. Smoothed Analysis ist eine Alternative zur Worst-Case-Analyse, die oft zu realistischeren Ergebnissen führt und so die praktische Performance von Algorithmen theoretisch untermauert. Sie ist eine Mischung aus Worst-Case- und Average-Case-Analyse, bei der die Performance auf Eingaben gemessen wird, die zufälliges Rauschen enthalten. Wir geben einen Einblick in Smoothed Analysis anhand zweier Beispiele: der k-Means-Methode für das Clustering-Problem und dem Nemhauser/Ullmann-Algorithmus für das Rucksack-Problem.

Keywords: smoothed analysis; probabilistic analysis; analysis of algorithms

* Correspondence address: University of Twente, Department of Applied Mathematics, P. O. Box 217, 7500 AE Enschede, Niederlande,


Published Online: 2011-12-01

Published in Print: 2011-12-01


Citation Information: it - Information Technology Methoden und innovative Anwendungen der Informatik und Informationstechnik. Volume 53, Issue 6, Pages 280–286, ISSN (Print) 1611-2776, DOI: https://doi.org/10.1524/itit.2011.0654, December 2011

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[1]
Markus Bläser, Bodo Manthey, and B. V. Raghavendra Rao
Algorithmica, 2013, Volume 66, Number 2, Page 397

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