Multigrid Algorithms on the Hypercube Multiprocessor
IEEE Transactions on Computers
Data movement techniques for the pyramid computer
SIAM Journal on Computing
Communication effect basic linear algebra computations on hypercube architectures
Journal of Parallel and Distributed Computing
Pyramidal systems for computer vision
Pyramidal systems for computer vision
Parallel, hierarchical software/hardware pyramid architectures
Pyramidal systems for computer vision
Pyramidal systems for computer vision
On Embedding Rectangular Grids in Hypercubes
IEEE Transactions on Computers
Embedding grids into hypercubes
VLSI Algorithms and Architectures
Spanning balanced trees in Boolean cubes
SIAM Journal on Scientific and Statistical Computing
Optimum Broadcasting and Personalized Communication in Hypercubes
IEEE Transactions on Computers
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
X-Tree: A tree structured multi-processor computer architecture
ISCA '78 Proceedings of the 5th annual symposium on Computer architecture
Embedding trees in the hypercube
Embedding trees in the hypercube
Combinatorial Algorithms: Theory and Practice
Combinatorial Algorithms: Theory and Practice
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A P(k, d) hyper-pyramid is a level structure of k Boolean cubes where the cube at level i is of dimension id, and a node at level i - 1 connects to every node in a d dimensional Boolean subcube at level i, except for the leaf level k. Hyper-pyramids contain pyramids as proper subgraphs. We show that a P(k, d) hyper-pyramid can be embedded in a Boolean cube with minimal expansion and dilation d. The congestion is bounded from above by 2d+1/d+2 and from below by 1 + ⌈2d-d/kd+1⌉. For P(k, 2) hyper-pyramids we present a dilation 2 and congestion 2 embedding. As a corollary a complete n-ary tree can be embedded in a Boolean cube with dilation max(2, ⌈log2 n⌉) and expansion 2k⌈log2 n⌉ + 1/nk+1-1/n-1. We also discuss multiple pyramid embeddings.