An Efficient Algorithm for Embedding Two-Dimensional Tori into Balanced Hypercubes

Balanced hypercube is a variant of the hypercube structure; it offers desirable properties such as connectivity, diameter, and fault-tolerance. Cycles and tori are popular interconnection topologies and have been widely used in distributed-memory parallel computers. Scholars have developed diverse and numerous parallel algorithms of cycles and tori. This paper proposes an efficient algorithm, called reflected edge label sequence, to generate cycle structures in balanced hypercubes. With this algorithm, we can embed cycles of length 2(2k+1), 1 <= k < n, into an n-dimensional balanced hypercube. The corresponding algorithm for embedding 2-dimensional 2(2k) x 2(2k) tori can be constructed on the basis of this approach, and the time complexity is linear with respect to the size of a balanced hypercube.