Optimal parallel sorting in multi-level storage

We adapt the Sharesort algorithm of Cypher and Plaxton to run on various parallel models of multi-level storage, and analyze its resulting performance. Sharesort was originally defined in the context of sorting n records on an n-processor hypercubic network. In that context, it is not known whether Sharesort is asymptotically optimal. Nonetheless, we find that Sharesort achieves optimal time bounds for parallel sorting in multi-level storage, under a variety of models that have been defined in the literature.