Uniformization of discrete data

Abstract

Some kind of discrete data sets can be practically transformed into uniform by the related distribution function. By addressing the sparsity of data which measures the discreteness, this paper demonstrates that the sparsity decides the uniformity of the transformed data, and that could be a good reason to explain both the success of the bucket sort in PennySort 2003 and the failure for the same algorithm with the data modified. So the sparsity provides a good criterion to predict whether the algorithm works or not. © Springer-Verlag Berlin Heidelberg 2005.