http://hdl.handle.net/10468/1366 2017-10-30T17:28:09Z http://hdl.handle.net/10468/1368 Modular smoothed analysis Schellekens, Michel P.; Hennessy, Aoife; Shi, Bichen Spielman’s smoothed complexity - a hybrid between worst and average case complexity measures - relies on perturbations of input instances to determine where average-case behavior turns to worst-case. The paper proposes a method supporting modular smoothed analysis. The method, involving a novel permutation model, is developed for the discrete case, focusing on randomness preserving algorithms. This approach simplifies the smoothed analysis and achieves greater precession in the expression of the smoothed complexity, where a recurrence equation is obtained as opposed to bounds. Moreover, the approach addresses, in this context, the formation of input instances–an open problem in smoothed complexity. To illustrate the method, we determine the modular smoothed complexity of Quicksort. 2014-01-01T00:00:00Z http://hdl.handle.net/10468/1367 Modular smoothed analysis of median-of-three Quicksort Hennessy, Aoife; Schellekens, Michel P. Spielman’s smoothed complexity - a hybrid between worst and average case complexity measures - relies on perturbations of input instances to determine where average-case behavior turns to worst-case. This approach simplifies the smoothed analysis and achieves greater precession in the expression of the smoothed complexity, where a recurrence equation is obtained as opposed to bounds. Moreover, the approach addresses, in this context, the formation of input instances–an open problem in smoothed complexity. In [23], we proposed a method supporting modular smoothed analysis and illustrated the method by determining the modular smoothed complexity of Quicksort. Here, we use the modular approach to calculate the median of three variant and compare these results with those in [23]. 2014-01-01T00:00:00Z