Some Topological Properties of the Honeycomb Rhombic Torus Based on Cayley Graph

Honeycomb tori are attractive alternatives to torus due to the smaller node degree, leading to lower complexity and lower implementation cost. The honeycomb networks are Cayley graphs with excellent topological properties. However, some topological properties of the honeycomb rhombic tori, such as internode distance, routing algorithm and broadcasting algorithm, are not developed. In this paper, we analyze the distance between any two nodes in the honeycomb rhombic tori and present an optimal routing algorithm for this class of networks. The algorithm is fully distributed, which can construct the shortest path between any pair of vertices. A broadcasting algorithm is also presented.

[1]  Sheldon B. Akers,et al.  A Group-Theoretic Model for Symmetric Interconnection Networks , 1989, IEEE Trans. Computers.

[2]  Wenjun Xiao,et al.  A Group Construction Method with Applications to Deriving Pruned Interconnection Networks , 2007, IEEE Transactions on Parallel and Distributed Systems.

[3]  Ivan Stojmenovic,et al.  Honeycomb Networks: Topological Properties and Communication Algorithms , 1997, IEEE Trans. Parallel Distributed Syst..

[4]  Arnold L. Rosenberg,et al.  Group Action Graphs and Parallel Architectures , 1990, SIAM J. Comput..

[5]  Wenjun Xiao,et al.  Structural properties of Cayley digraphs with applications to mesh and pruned torus interconnection networks , 2007, J. Comput. Syst. Sci..

[6]  Li-Yen Hsu,et al.  Generalized honeycomb torus , 2003, Inf. Process. Lett..

[7]  N. Biggs.  Algebraic Graph Theory , 1974 .

[8]  Wenjun Xiao,et al.  Further mathematical properties of Cayley digraphs applied to hexagonal and honeycomb meshes , 2007, Discret. Appl. Math..

[9]  Xiaofan Yang,et al.  Fault-Tolerant Ring Embedding in a Honeycomb Torus with Node Failures , 1999, Parallel Process. Lett..

[10]  Jean Frédéric Myoupo,et al.  All-to-All Broadcasting Algorithms on Honeycomb Networks and Applications , 1999, Parallel Process. Lett..

[11]  Behrooz Parhami,et al.  A Unified Formulation of Honeycomb and Diamond Networks , 2001, IEEE Trans. Parallel Distributed Syst..

[12]  Xiaofan Yang,et al.  Honeycomb tori are Hamiltonian , 1999, Inf. Process. Lett..

[13]  Brian Alspach,et al.  Honeycomb toroidal graphs are Cayley graphs , 2009, Inf. Process. Lett..