Embedding a family of meshes into twisted cubes

Embedding a k-D Torus into a Locally Twisted Cube

“…For instance, Fan and Jia [5] proposed that a 2-D mesh of size 2 × 2 n−1 and a family of two disjoint 2-D meshes of size 4 × 2 n−3 can be totally embedded into an n-dimensional (n-D) crossed cube with unit dilation, respectively. Recently, Lai and Tsai [6], [16] proved that an n-D Twisted cube and n-D Möbius cube have the same result those of the n-D crossed cube, respectively. Dong et al [3] showed that a family of two (four, respectively) disjoint 3-D meshes of size 2 × 2 × 2 n−3 (4 × 2 × 2 n−5 , respectively) each can be embedded in an n-D crossed cube with unit dilation.…”

Cycles Embedding of Twisted Cubes

“…Actually, cycles are also popularly used interconnection networks in distributed-memory parallel computers. Furthermore, the problem of how to embed cycles into a host graph has received a great deal of attention steadily in academia [6], [7], [11], [16], [17], [23] as well as industries in recent years.…”

“…However, the diameter, wide diameter, and faulty diameter in twisted cubes are about half of those in comparable hypercubes [5]. The problem of embedding linear arrays and cycles into T Q n has attracted substantial attention [5], [6], [9], [10], [11], [16], [24] in recent years. In this paper, our attention is restricted to ideal embedding (with unit dilation) and further provide two kinds of systematic methods of embedding cycles into T Q n .…”

Embedding meshes into twisted-cubes

“…Graph embedding has significant applications in transplanting parallel algorithms developed for one network to a different one, and allocating concurrent processes to processors in the network. As the popular interconnection networks used in parallel computing, meshes [8,10,16,17,23,28], paths (or linear arrays) [7,[12][13][14][15]22,25,26,32], cycles [2][3][4]6,18,19,29,30], and trees [5,9,33] are the fundamental guest graphs.…”

“…Therefore, embedding of meshes is a very important issue in interconnection networks. In particular, many results on embedding of meshes into variations of hypercubes have been obtained in recent years [8,10,16,17,23].…”