Large-Scale Sorting in Uniform Memory Hierarchies

We present several e cient algorithms for sorting on the uniform memory hierarchy (UMH), introduced by Alpern, Carter, and Feig, and its paral- lelization P-UMH.We give optimal and nearly-optimal algorithms for a wide range of bandwidth degradations, including a parsimonious algorithm for constant bandwidth. We also develop optimal sorting algorithms for all bandwidths for other versions of UMH and P-UMH, including natural restrictions we introduce called RUMH and P-RUMH, which more closely correspond to current programming languages