How to Systematically Embed Cycles in Balanced Hypercubes

The balanced hypercube is a variant of the hypercube structure and has desirable properties like connectivity, regularity, and symmetry. The cycle is a popular interconnection topology and has been widely used in distributed-memory parallel computers. Moreover, parallel algorithms of cycles have been extensively developed and used. The problem of how to embed cycles into a host graph has attracted a great attention in recent years. However, there is no systematic method proposed to generate the desired cycles in balanced hypercubes. In this paper, the authors develop systematic linear time algorithm to construct cycles and Hamiltonian cycles for the balanced hypercube.