Minimum wirelength of hypercubes into n-dimensional grid networks

In the paper [Exact wirelength of hypercube on a grid, Discrete Applied Mathematics 157 (7) (2009) 1486–1495], the minimum wirelength of an r  -dimensional hypercube into a 2⌊r/2⌋×2⌈r/2⌉2⌊r/2⌋×2⌈r/2⌉ grid has been obtained. In this paper, we obtain the same when the 2⌊r/2⌋×2⌈r/2⌉2⌊r/2⌋×2⌈r/2⌉ rectangular grid is replaced by a generalized grid of size 2r1×2r2×⋯×2rn2r1×2r2×⋯×2rn where r1+r2+⋯+rn=rr1+r2+⋯+rn=r, r1⩽r2⩽⋯⩽rnr1⩽r2⩽⋯⩽rn.

► We discuss the lexicographic embedding. ► We study the changes in the composite sets of hypercubes. ► We attain the minimum wirelength of hypercubes into n-dimensional grid networks in linear time.