Optimal Routing Algorithms for Generalized de Bruijn Digraphs

Generalized de Bruijn digraph, G_{B}(d,n), was proposed independently by Imase and Itoh, and Reddy, Pradhan and Kuhl to include any number of nodes. Du and Hwang showed that G_{B}(d, n) essentially retains all the nice properties of de Bruijn digraphs, and presented a \left\lceil {\log _d n} \right\rceil -step routing algorithm, where d is the indegree and outdegree, and n is the number of nodes in the graph.

[1]  Ming-Syan Chen,et al.  Depth-First Search Approach for Fault-Tolerant Routing in Hypercube , 1990, IEEE Trans. Parallel Distributed Syst..

[2]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[3]  Makoto Imase,et al.  Connectivity of Regular Directed Graphs with Small Diameters , 1985, IEEE Transactions on Computers.

[4]  Makoto Imase,et al.  A Design for Directed Graphs with Minimum Diameter , 1983, IEEE Transactions on Computers.

[5]  Arunabha Sen,et al.  On Fault-Tolerant Distributor Communication Architecture , 1986, IEEE Transactions on Computers.

[6]  X.-N. Tan,et al.  Optimal routing in the shuffle-exchange networks for multiprocessor systems , 1988, [Proceedings] COMPEURO 88 - System Design: Concepts, Methods and Tools.

[7]  de Ng Dick Bruijn.  A combinatorial problem , 1946 .

[8]  Dhiraj K. Pradhan,et al.  A Fault-Tolerant Communication Architecture for Distributed Systems , 1982, IEEE Transactions on Computers.

[9]  Makoto Imase,et al.  Design to Minimize Diameter on Building-Block Network , 1981, IEEE Transactions on Computers.

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

[11]  Ding-Zhu Du,et al.  Generalized de Bruijn digraphs , 1988, Networks.

[12]  Sam Toueg,et al.  On the impossibility of Directed Moore Graphs , 1980, J. Comb. Theory, Ser. B.

[13]  Dhiraj K. Pradhan,et al.  The De Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI , 1989, IEEE Trans. Computers.

[14]  C. Y. Roger Chen,et al.  Optimal Routing Algorithm and the Diameter of the Cube-Connected Cycles , 1993, IEEE Trans. Parallel Distributed Syst..