This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Efficient Communication Algorithms in Hexagonal Mesh Interconnection Networks
January 2012 (vol. 23 no. 1)
pp. 69-77
B. Albader, Dept. of Comput. Sci., Kuwait Univ., Safat, Kuwait
B. Bose, Sch. of Electr. Eng. & Comput. Sci., Oregon State Univ., Corvallis, OR, USA
M. Flahive, Dept. of Math., Oregon State Univ., Corvallis, OR, USA
In this paper, we show that the hexagonal mesh networks developed in the early 1990s are a special case of the EJ networks that have been considered more recently. Using a node addressing scheme based on the EJ number system, we give a shortest path routing algorithm for hexagonal mesh networks. We also extend the known efficient one-to-all broadcasting algorithm on hexagonal mesh networks to algorithms for one-to-one personalized broadcasting, all-to-all broadcasting, and all-to-all personalized broadcasting algorithms. Their time complexity and optimality are analyzed.

[1] N.R. Adiga et al., “An Overview of the BlueGene/L Supercomputer,” Proc. ACM/IEEE Conf. Supercomputing, 2002.
[2] D.P. Bertekas and J.N. Tsitskilis, Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, 1989.
[3] B. Bose, B. Broeg, Y. Kwon, and Y. Ashir, “Lee Distance and Topological Properties of $k$ -ary $n$ -Cubes,” IEEE Trans. Computers, vol. 44, no. 8, pp. 1021-1030, Aug. 1995.
[4] M.-S. Chen, K.G. Shin, and D.D. Kandlur, “Addressing, Routing, and Broadcasting in Hexagonal Mesh Multiprocessors,” IEEE Trans. Computers, vol. 39, no. 1, pp. 10-18, Jan. 1990.
[5] S. Costa, M. Muniz, E. Agustini, and R. Palazzo, “Graphs, Tessellations, and Perfect Codes on Flat Tori,” IEEE Trans. Information Theory, vol. 50, no. 10, pp. 2363-2377, Oct. 2004.
[6] J.W. Dolter, P. Ramanathan, and K.G. Shin, “Performance Analysis of Virtual Cut-Through Switching in HARTS: A Hexagonal Mesh Multicomputer,” IEEE Trans. Computers, vol. 40, no. 6, pp. 669-680, June 1991.
[7] M. Flahive and B. Bose, “Topological Properties of Quadratic Interconnection Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 21, no. 8, pp. 1132-1142, Aug. 2010.
[8] F. Garcia, I. Stojmenovic, and J. Zhang, “Addressing and Routing in Hexagonal Networks with Applications in Location Update and Connection Rerouting in Mobile Phone Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 13, no. 9, pp. 963-971, Sept. 2002.
[9] K. Huber, “Codes over Gaussian Integers,” IEEE Trans. Information Theory, vol. 40, no. 1, pp. 207-216, Jan. 1994.
[10] K. Huber, “Codes over Eisenstein-Jacobi Integers,” Finite Fields: Theory, Applications, and Algorithms, pp. 165-179, AMS Bookstore, 1994.
[11] D.D. Kandlur and K.G. Shin, “Reliable Broadcast Algorithms for HARTS,” ACM Trans. Computer Systems, vol. 9, pp. 374-398, 1991.
[12] V. Kumar et al., Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin-Cummings Publishing Company, 1994.
[13] C. Martínez, E. Vallejo, R. Beivide, C. Izu, and M. Moretó, “Dense Gaussian Networks: Suitable Topologies for On-Chip Multiprocessors,” Int'l J. Parallel Processing, vol. 34, pp. 193-211, 2006.
[14] C. Martínez, R. Beivide, E. Stafford, M. Moretó, and E. Gabidulin, “Modeling Toroidal Networks with the Gaussian Integers,” IEEE Trans. Computers, vol. 57, no. 8, pp. 1046-1056, Aug. 2008.
[15] C. Martínez, E. Stafford, R. Beivide, and E.M. Gabidulin, “Modeling Hexagonal Networks with the Eisenstein-Jacobi Graphs,” Problems of Information Transmission, vol. 44, pp. 1-11, 2008.
[16] M.D. Noakes, D.A. Wallach, and W.J. Dally, “The J-Machine Multicomputer: An Architectural Evolution,” ACM Sigarch Computer Architecture News, vol. 21, no. 2, pp. 224-235, 1993.
[17] W. Oed, “Massively Parallel Processor System CRAY T3D,” technical report, Cray Research GmbH, Nov. 1993.
[18] C.L. Seitz, “Submicron Systems Architecture Project Semi-Annual Technical Report,” Technical Report Caltec-CS-88-18, California Inst. of Tech nology, 1988.
[19] Tera Computer Systems, Overview of the Tera Parallel Computer, 1993.

Index Terms:
Routing,Broadcasting,Mesh networks,Multiprocessor interconnection,Topology,Algorithm design and analysis,communication algorithms.,Parallel processing,interconnection networks,hexagonal mesh networks,EJ networks,broadcasting
Citation:
B. Albader, B. Bose, M. Flahive, "Efficient Communication Algorithms in Hexagonal Mesh Interconnection Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 23, no. 1, pp. 69-77, Jan. 2012, doi:10.1109/TPDS.2011.112
Usage of this product signifies your acceptance of the Terms of Use.