Results 211 to 220 of about 68,163 (244)
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2006
In this paper we propose a semi-distributed self-diagnostic algorithm for Hypercube networks which is based on the use of a combinatorial structure known as the Hadamard matrix. We propose a model for providing fault- tolerance to the diagnostic scheme and to analyze the performance of the proposed diagnostic scheme.
Arif Ghafoor, Patrick Solé
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In this paper we propose a semi-distributed self-diagnostic algorithm for Hypercube networks which is based on the use of a combinatorial structure known as the Hadamard matrix. We propose a model for providing fault- tolerance to the diagnostic scheme and to analyze the performance of the proposed diagnostic scheme.
Arif Ghafoor, Patrick Solé
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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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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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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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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
Summary: 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 \(\alpha\). We show that the \(k\)-cube \(Q_{k}\) is isomorphic to the direct product \(G \times H\)
Bostjan Bresar +3 more
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Summary: 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 \(\alpha\). We show that the \(k\)-cube \(Q_{k}\) is isomorphic to the direct product \(G \times H\)
Bostjan Bresar +3 more
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Classifying Hyperplanes in Hypercubes
SIAM Journal on Discrete Mathematics, 1996Summary: We 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 \(d\)
Oswin Aichholzer, Franz Aurenhammer
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2012
We define hypercubes of duality—of which the modern square of opposition is an emblematic example—in proper mathematical terms, as orbits under some action of the additive group \(\mathbb{Z}_{2}^{m}\), with m∈ℕ. We then introduce a notion of dimension for duality in classical logic and show, for example, how propositional expressions in at most three ...
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We define hypercubes of duality—of which the modern square of opposition is an emblematic example—in proper mathematical terms, as orbits under some action of the additive group \(\mathbb{Z}_{2}^{m}\), with m∈ℕ. We then introduce a notion of dimension for duality in classical logic and show, for example, how propositional expressions in at most three ...
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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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