Perfect Distance-d Placements in 2D Toroidal Networks

A perfect distance-d placement distributes a limited number of resources in a multicomputer parallel system so that every non-resource node is within a distance d or less from exactly one resource node. In this paper, we prove a necessary and sufficient condition for the existence of perfect distance-d placements in 2D toroidal networks. Furthermore, we describe how to generate these placements when they exist.

[1]  Yaagoub Ashir,et al.  Lee Distance and Topological Properties of k-ary n-cubes , 1995, IEEE Trans. Computers.

[2]  Nian-Feng Tzeng,et al.  Fault-Tolerant Resource Placement in Hypercube Computers , 1991, ICPP.

[3]  Charles L. Seitz.  Submicron Systems Architecture Project: Semiannual Technical Report , 1989 .

[4]  Steven L. Scott,et al.  The Cray T3E Network: Adaptive Routing in a High Performance 3D Torus , 1996 .

[5]  Hsing-Lung Chen,et al.  Efficient Resource Placement in Hypercubes Using Multiple-Adjacency Codes , 1994, IEEE Trans. Computers.

[6]  Prithviraj Banerjee,et al.  Design, Analysis, and Simulation of I/O Architectures for Hypercube , 1990, IEEE Trans. Parallel Distributed Syst..

[7]  Parameswaran Ramanathan,et al.  Resource Placement with Multiple Adjacency Constraints in k-ary n-Cubes , 1995, IEEE Trans. Parallel Distributed Syst..

[8]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[9]  Bella Bose,et al.  Resource placements in 2D tori , 1998, Proceedings of the First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processing.

[10]  Myung M. Bae,et al.  Spare processor allocation for fault tolerance in torus-based multicomputers , 1996, Proceedings of Annual Symposium on Fault Tolerant Computing.

[11]  Odysseas I. Pentakalos.  An Introduction to the InfiniBand Architecture , 2002, Int. CMG Conference.

[12]  Quentin F. Stout,et al.  PERFECT DOMINATING SETS , 1990 .

[13]  Parameswaran Ramanathan,et al.  Resource Placement in k-Ary n-Cubes , 1992, ICPP.

[14]  M. Livingston,et al.  Distributing resources in hypercube computers , 1988, C3P.

[15]  Charles L. Seitz,et al.  The design of the Caltech Mosaic C multicomputer , 1993 .

[16]  Alain J. Martin,et al.  The architecture and programming of the Ametek series 2010 multicomputer , 1988, C3P.

[17]  Nian-Feng Tzeng,et al.  Resource Allocation in Cube Network Systems Based on the Covering Radius , 1996, IEEE Trans. Parallel Distributed Syst..

[18]  Myung M. Bae,et al.  Resource placement in torus-based networks , 1996, Proceedings of International Conference on Parallel Processing.

[19]  Gregory F. Pfister,et al.  Aspects of the InfiniBand architecture , 2001, Proceedings 42nd IEEE Symposium on Foundations of Computer Science.

[20]  Bella Bose,et al.  On resource placements in 3D tori , 2003, J. Parallel Distributed Comput..