Constructing Sorting Networks from k-Sorters

We study the problem of using sorters of k values to form large sorting and merging networks. For n an integral power of k, we show how to merge k sorted vectors of length nk each using 4logkn-3 layers of k-sorters and 4logk n-5 layers of k-input binary mergers. As a result, we show how to sort n values using 2log2kn-logkn layers of k-sorters and 2log2kn-3logkn+1 layers of k-input binary mergers.