Diagonal and Toroidal Mesh Networks

Diagonal and toroidal mesh are degree-4 point to point interconnection models suitable for connecting communication elements in parallel computers, particularly multicomputers. The two networks have a similar structure. The toroidal mesh is popular and well-studied whereas the diagonal mesh is relatively new. In this paper, we show that the diagonal mesh has a smaller diameter and a larger bisection width. It also retains advantages such as a simple rectangular structure, wirability and scalability of the toroidal mesh network. An optimal self-routing algorithm is developed for these networks. Using this algorithm and the existing routing algorithm for the toroidal mesh, we simulated and compare the performance of these two networks with N=35/spl times/71=2485, N=49/spl times/99=4851, and N=69/spl times/139=9591 nodes under a constant system with a fixed number of messages. Deflection routing is used to resolve conflicts. The effects of various deflection criteria are also investigated. We show that the diagonal mesh outperforms the toroidal mesh in all cases, and thus provides an attractive alternative to the toroidal mesh network. >

[1]  C. Thomborson,et al.  Area-time complexity for VLSI , 1979, STOC.

[2]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[3]  Flaminio Borgonovo,et al.  Locally-optimal deflection routing in the Bidirectional Manhattan Network , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[4]  Mondher Ben-Ayed.  Dynamic routing for regular direct computer networks , 1990 .

[5]  Tse-yun Feng,et al.  A Survey of Interconnection Networks , 1981, Computer.

[6]  P. Baran,et al.  On Distributed Communications Networks , 1964 .

[7]  Bruce E. Hajek,et al.  Performance of shuffle-like switching networks with deflection , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[8]  Allan Gottlieb,et al.  Highly parallel computing , 1989, Benjamin/Cummings Series in computer science and engineering.

[9]  Kit-Ming Wendy Tang.  Dense, symmetric interconnection networks , 1991 .

[10]  Nicholas F. Maxemchuk,et al.  Routing in the Manhattan Street Network , 1987, IEEE Trans. Commun..

[11]  N. F. Maxemchuk,et al.  Regular mesh topologies in local and metropolitan area networks , 1985, AT&T Technical Journal.

[12]  K. Wendy Tang,et al.  Vertex-transitivity and routing for Cayley graphs in GCR representations , 1992, SAC '92.

[13]  Dennis Parkinson,et al.  Massively parallel computing with the DAP , 1990 .

[14]  K. Wendy Tang,et al.  Routing and Diameter Analysis of Diagonal Mesh Networks , 1992, ICPP.

[15]  Nicholas F. Maxemchuk,et al.  Comparison of deflection and store-and-forward techniques in the Manhattan Street and Shuffle-Exchange Networks , 1989, IEEE INFOCOM '89, Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies.

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

[17]  Charles Delorme,et al.  Strategies for Interconnection Networks: Some Methods from Graph Theory , 1986, J. Parallel Distributed Comput..

[18]  Larry D. Wittie,et al.  Communication Structures for Large Networks of Microcomputers , 1981, IEEE Transactions on Computers.

[19]  Paolo Giacomazzi,et al.  Shuffle interconnection networks with deflection routing for ATM switching: The Closed-Loop Shuffleout , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.