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Q.M. Malluhi, M.A. Bayoumi, "The Hierarchical Hypercube: A New Interconnection Topology for Massively Parallel Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 1, pp. 1730, January, 1994.  
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@article{ 10.1109/71.262585, author = {Q.M. Malluhi and M.A. Bayoumi}, title = {The Hierarchical Hypercube: A New Interconnection Topology for Massively Parallel Systems}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {5}, number = {1}, issn = {10459219}, year = {1994}, pages = {1730}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.262585}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  The Hierarchical Hypercube: A New Interconnection Topology for Massively Parallel Systems IS  1 SN  10459219 SP17 EP30 EPD  1730 A1  Q.M. Malluhi, A1  M.A. Bayoumi, PY  1994 KW  Index Termsparallel algorithms; computational complexity; hypercube networks; hierarchicalhypercube; interconnection topology; massively parallel systems; performance;symmetry; logarithmic diameter; onetoone transfer; onetoall broadcasting; divide &conquer class; parallels; time complexity VL  5 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Interconnection networks play a crucial role in the performance of parallel systems. Thispaper introduces a new interconnection topology that is called the hierarchical hypercube(HHC). This topology is suitable for massively parallel systems with thousands ofprocessors. An appealing property of this network is the low number of connections perprocessor, which enhances the VLSI design and fabrication of the system. Other alluringfeatures include symmetry and logarithmic diameter, which imply easy and fast algorithms for communication. Moreover, the HHC is scalable; that is it can embed HHC's of lower dimensions. The paper presents two algorithms for data communication in the HHC. The first algorithm is for onetoone transfer, and the second is for onetoall broadcasting. Both algorithms take O(log/sub 2/k), where k is the total number of processors in the system. A wide class of problems, the divide & conquer class (D&Q), is shown to be easily and efficiently solvable on the HHC topology. Parallel algorithms are provided to describe how a D&Q problem can be solved efficiently on an HHC structure. The solution of a D&Q problem instance having up to k inputs requires a time complexity of O(log/sub 2/k).
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