Optimally Embedding 3-Ary n-Cubes into Grids

The 3-ary n-cube, denoted as Qn3, is an important interconnection network topology proposed for parallel computers, owing to its many desirable properties such as regular and symmetrical structure, and strong scalability, among others. In this paper, we first obtain an exact formula for the minimum wirelength to embed Qn3 into grids. We then propose a load balancing algorithm for embedding Qn3 into a square grid with minimum dilation and congestion. Finally, we derive an O(N²) algorithm for embedding Qn3 into a gird with balanced communication, where N is the number of nodes in Qn3. Simulation experiments are performed to verify the total wirelength and evaluate the network cost of our proposed embedding algorithm.