PDM sorting algorithms that take a small number of passes

We live in an era of data explosion that necessitates the discovery of novel out-of-core techniques. The I/O bottleneck has to be dealt with in developing out-of-core methods. The parallel disk model (PDM) has been proposed to alleviate the I/O bottleneck. Sorting is an important problem that has ubiquitous applications. Several asymptotically optimal PDM sorting algorithms are known and now the focus has shifted to developing algorithms for problem sizes of practical interest. In this paper we present several novel algorithms for sorting on the PDM that take only a small number of passes through the data. We also present a generalization of the zero-one principle for sorting. A shuffling lemma is presented as well. These lemmas should be of independent interest for average case analysis of sorting algorithms as well as for the analysis of randomized sorting algorithms.