A novel algorithm to embed a multi-dimensional torus into a locally twisted cube

AbstractThis paper addresses how to embed a multi-dimensional torus of maximal size of into an n-dimensional locally twisted cube. The major contribution of this paper is that, for n≥4, every k-dimensional torus of size 2s1×2s2×⋯×2sk satisfying ∑i=1ksi=n can be embedded into an n-dimensional locally twisted cube with dilation 2 and unit expansion. Further, an embedding algorithm can be constructed based on our embedding method, and the time complexity of this algorithm is linear with respect to the size of the locally twisted cube. The embedding is optimal in the sense that it has unit expansion