Prefix Computation and Sorting in Dual-Cube

In this paper, we describe two algorithmic techniques for the design of efficient algorithms in dual-cube. The first uses cluster structure of dual-cube, and the second uses recursive structure of the dual-cube. We propose efficient algorithms for parallel prefix computation and sorting in dual-cube based on the two techniques, respectively. For a dual-cube D_n with 2^2n-1 nodes and n links per node, the communication and computation times of the algorithm for parallel prefix computation are at most 2n+1 and 4n-2, respectively; and those of the algorithm for sorting are at most 6n² and 2n², respectively.