Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Stretching a Knock-Knee Layout for Multilayer Wiring
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Theoretical aspects of VLSI pin limitations
SIAM Journal on Computing
IEEE Transactions on Parallel and Distributed Systems
Enabling technologies for petaflops computing
Enabling technologies for petaflops computing
Designing Clustered Multiprocessor Systems under Packaging and Technological Advancements
IEEE Transactions on Parallel and Distributed Systems
Efficient VLSI Layouts for Homogeneous Product Networks
IEEE Transactions on Computers
Layout of the batcher bitonic sorter (extended abstract)
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Compact grid layouts of multi-level networks
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
VLSI layouts of complete graphs and star graphs
Information Processing Letters
Some compact layouts of the butterfly
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Tighter Layouts of the Cube-Connected Cycles
IEEE Transactions on Parallel and Distributed Systems
Introduction to Parallel Processing: Algorithms and Architectures
Introduction to Parallel Processing: Algorithms and Architectures
The Recursive Grid Layout Scheme for VLSI Layout of Hierarchical Networks
IPPS '99/SPDP '99 Proceedings of the 13th International Symposium on Parallel Processing and the 10th Symposium on Parallel and Distributed Processing
VLSI Architecture: Past, Present, and Future
ARVLSI '99 Proceedings of the 20th Anniversary Conference on Advanced Research in VLSI
Efficient VLSI Layouts of Hypercubic Networks
FRONTIERS '99 Proceedings of the The 7th Symposium on the Frontiers of Massively Parallel Computation
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
A complexity theory for VLSI
Efficient low-degree interconnection networks for parallel processing: topologies, algorithms, vlsi layouts, and fault tolerance
AT2L2 o N2/2 for fast fourier transform in multilayer VLSI
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
On the VLSI Area and Bisection Width of Star Graphs and Hierarchical Cubic Networks
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Multilayer VLSI Layout for Interconnection Networks
ICPP '00 Proceedings of the Proceedings of the 2000 International Conference on Parallel Processing
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We present a scheme for optimal VLSI layout and packaging of butterfly networks under the Thompson model, the multilayer grid model, and the hierarchical layout model. We show that when L layers of wires are available, an N-node butterfly network can be laid out with area 4N2/L2 log22 N + o (N2/L2 log2 N), maximum wire length 2N/L log2 N + o (N/L log N), and volume 4N2/L log22 N + o (N2/L log2 N) , under the multilayer 2-D grid model, where only one active layer (for network nodes) is required and L layers of wires are available. Our layout scheme allows us to partition an N-node butterfly network into &THgr;(N1-1/l N)-node clusters with an average of dic ≈ 4l-4/log2 N (=O(1/log N) for any constant integer l) inter-cluster links per node, leading to optimal layout and packaging at the same time under the hierarchical layout model. The scalability of our layouts are optimal in that we can allow each of O(N/ log N) nodes to occupy an area as large as o (N/L2 log N) and each of the remaining N - o(N) network nodes to occupy an area as large as o (N/L2 log2 N), without increasing the leading constants of layout area, volume, or maximum wire length.