On the fault-tolerant embeddings of complete binary trees in the mesh interconnection networks

Embedding meshes into crossed cubes

“…Recently, many interconnection networks and their properties have been studied in the literature [2,4,[9][10][11][12][13][14][15][16][19][20][21][22][23][24][25]29].…”

“…Many applications, such as architecture simulations and processor allocations, can be modelled as graph embeddings [1,2,9,11,[13][14][15][23][24][25]27]. Let GðV ; EÞ denote a graph, where V ðGÞ and EðGÞ are the node set and the edge set of G, respectively.…”

“…[1,2,9,[11][12][13][14][15]18,20,[23][24][25][26][27], because they are the common data structures or interconnection structures used in parallel computing. The crossed cube is a variant of the hypercube, but has some better features than the hypercube, such as shorter diameter [3,5].…”

Longest fault-free paths in hypercubes with vertex faults

“…Since processor or link faults may develop in real world networks, it is important to consider faulty networks. The problems of diameter [4], routing [6], multicasting [13], broadcasting [16], gossiping [5], and embedding [7,12,17] have been solved in various faulty networks. This study considers the problem of fault-tolerant embedding.…”

Embedding a family of meshes into twisted cubes

“…The expansion is defined as the ratio of the number of vertices in the host graph to the number of vertices in the guest graph. Architecture simulation can be modelled as a graph embedding, which embeds the guest architecture into the host architecture of the simulation [2][3][4][5]7,9].…”