Directed hamiltonian packing in d-dimensional meshes and its application

A digraph G with minimum in-degree d and minimum out-degree d is said to have a directed hamiltonian packing if G has d link-disjoint directed hamiltonian cycles. We show that a d-dimensional N-1 x ... x N-d mesh, when N-i greater than or equal to 2d is even, has a directed hamiltonian packing, where an edge (u,v) in G is regarded as two directed links [u,v] and [v,u]. As its application, we design a time-efficient all-to-all broadcasting algorithm in 3-dimensional meshes under the wormhole routing model.