Parallel Prefix Computation and Sorting on a Recursive Dual-Net

In this paper, we propose efficient algorithms for parallel prefix computation and sorting on a recursive dual-net. The recursive dual-net $RDN^k$(B) for k > 0 has $(2n_o)^{2K}/2$ nodes and $d_0$ + k links per node, where $n_0$ and $d_0$ are the number of nod es and the node-degree of the base-network B, respectively. Assume that each node holds one data item, the communication and computation time complexities of the algorithm for parallel prefix computation on $RDN^k$(B), k > 0, are $2^{k+1}-2+2^kT_{comm}(0)$ and $2^{k+1}-2+2^kT_{comp}(0)$, respectively, where $T_{comm}(0)$ and $T_{comp}(0)$ are the communication and computation time complexities of the algorithm for parallel prefix computation on the base-network B, respectively. The algorithm for parallel sorting on $RDN^k$(B) is restricted on B = $Q_m$ where $Q_m$ is an m-cube. Assume that each node holds a single data item, the sorting algorithm runs in $O((m2^k)^2)$ computation steps and $O((km2^k)^2)$ communication steps, respectively.