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2006 Canadian Conference on Electrical and Computer Engineering, 2006
Techniques for advanced logic design in spatial dimensions for the purposes of nano-devices and nanoICs are being formulated to incorporate topologies that satisfy certain requirements of nanotechnology. The hypercube is considered a relevant topology for this design.
Loyd Reed Hook, Samuel C. Lee
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Techniques for advanced logic design in spatial dimensions for the purposes of nano-devices and nanoICs are being formulated to incorporate topologies that satisfy certain requirements of nanotechnology. The hypercube is considered a relevant topology for this design.
Loyd Reed Hook, Samuel C. Lee
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IEEE Transactions on Parallel and Distributed Systems, 2005
This paper presents the exchanged hypercube, a new interconnection network obtained by systematically removing links from a binary hypercube. It maintains several desirable properties of the binary hypercube yet with reduced interconnection complexity.
Peter K. K. Loh +2 more
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This paper presents the exchanged hypercube, a new interconnection network obtained by systematically removing links from a binary hypercube. It maintains several desirable properties of the binary hypercube yet with reduced interconnection complexity.
Peter K. K. Loh +2 more
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SIAM Journal on Discrete Mathematics, 1989
This paper considers the following game on a hypercube, first suggested by Lagarias and Saks. Suppose $2^n$ pebbles are distributed onto vertices of an n-cube (with $2^n$ vertices). A pebbling step is to remove two pebbles from some vertex and then place one pebble at an adjacent vertex. The question of interest is to determine if it is possible to get
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This paper considers the following game on a hypercube, first suggested by Lagarias and Saks. Suppose $2^n$ pebbles are distributed onto vertices of an n-cube (with $2^n$ vertices). A pebbling step is to remove two pebbles from some vertex and then place one pebble at an adjacent vertex. The question of interest is to determine if it is possible to get
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Random Structures and Algorithms, 2005
A point \(p\) in \(\mathbb R^d\) is said to dominate another point \(q\) if the difference \(p-q\) has only nonnegative coordinates. The nondominated points in a set of points are called maxima. The interest of studying dominance and maxima is multifold. First, dominance represents one of the most natural partial orders for multidimensional points, and
Zhi-Dong Bai +3 more
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A point \(p\) in \(\mathbb R^d\) is said to dominate another point \(q\) if the difference \(p-q\) has only nonnegative coordinates. The nondominated points in a set of points are called maxima. The interest of studying dominance and maxima is multifold. First, dominance represents one of the most natural partial orders for multidimensional points, and
Zhi-Dong Bai +3 more
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IEEE Transactions on Computers, 1991
A hypercube with extra connections added between pairs of nodes through otherwise unused links is investigated. The extra connections are made in a way that maximizes the improvement of the performance measure of interest under various traffic distributions. The resulting hypercube, called the enhanced hypercube, requires a simple routing algorithm and
Nian-Feng Tzeng, Sizheng Wei
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A hypercube with extra connections added between pairs of nodes through otherwise unused links is investigated. The extra connections are made in a way that maximizes the improvement of the performance measure of interest under various traffic distributions. The resulting hypercube, called the enhanced hypercube, requires a simple routing algorithm and
Nian-Feng Tzeng, Sizheng Wei
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Journal of Graph Theory, 1984
AbstractAn induced subgraph G of a graph H is a retract of H if there is an edge‐preserving map f from H onto G such that f|G is the identity map on G. A median graph is a connected graph such that for any three vertices u,v and w, there exists a unique vertex x which lies simultaneously on some shortest (u,v)‐, (v,w)‐, and (w,u)‐paths.
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AbstractAn induced subgraph G of a graph H is a retract of H if there is an edge‐preserving map f from H onto G such that f|G is the identity map on G. A median graph is a connected graph such that for any three vertices u,v and w, there exists a unique vertex x which lies simultaneously on some shortest (u,v)‐, (v,w)‐, and (w,u)‐paths.
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SIAM Journal on Discrete Mathematics, 2005
Let G be a connected bipartite graph. An involution $\alpha$ of G that preserves the bipartition of G is called bipartite. Let $G^\alpha$ be the graph obtained from G by adding to G the natural perfect matching induced by $\alpha$.
Bostjan Bresar +3 more
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Let G be a connected bipartite graph. An involution $\alpha$ of G that preserves the bipartition of G is called bipartite. Let $G^\alpha$ be the graph obtained from G by adding to G the natural perfect matching induced by $\alpha$.
Bostjan Bresar +3 more
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Proceedings of the third conference on Hypercube concurrent computers and applications -, 1988
We describe a hypercube ray-tracing program for rendering computer graphics. For small models, which fit in the memory of a single processor, the ray-tracer uses a scattered decomposition of pixels to balance the load, and achieves a very high efficiency.
Salmon, John, Goldsmith, Jeff
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We describe a hypercube ray-tracing program for rendering computer graphics. For small models, which fit in the memory of a single processor, the ray-tracer uses a scattered decomposition of pixels to balance the load, and achieves a very high efficiency.
Salmon, John, Goldsmith, Jeff
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Classifying Hyperplanes in Hypercubes
SIAM Journal on Discrete Mathematics, 1996We consider hyperplanes spanned by vertices of the unit d-cube. We classify these hyperplanes by parallelism to coordinate axes, by symmetry of the d-cube vertices they avoid, as well as by so-called hull-honesty. (Hull-honest hyperplanes are those whose intersection figure with the d-cube coincides with the convex hull of the d-cube vertices they ...
Oswin Aichholzer, Franz Aurenhammer
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1992
New approach to the fragmentation problem of hypercube multiprocessors with dynamic allocation of subcubes is proposed. It is based on constructing Hamiltonian circuits of incomplete hypercubes. The main result is a constructive proof that an n-cube from which up to n−2 vertex-disjoint subcubes are removed so that it remains connected is a Hamiltonian ...
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New approach to the fragmentation problem of hypercube multiprocessors with dynamic allocation of subcubes is proposed. It is based on constructing Hamiltonian circuits of incomplete hypercubes. The main result is a constructive proof that an n-cube from which up to n−2 vertex-disjoint subcubes are removed so that it remains connected is a Hamiltonian ...
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