Smoothed analysis: analysis of algorithms beyond worst case

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.