Results 31 to 40 of about 68,163 (244)
Subcube embeddability and fault tolerance of augmented hypercubes
, 2008 Hypercube networks have received much attention from both parallel processing and communications areas over the years since they offer a rich interconnection structure with high bandwidth, logarithmic diameter, and high degree of fault tolerance.
Mohamed Yasim, Sithy Shameema
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Spin Glasses on the Hypercube [PDF]
, 2009 We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the
B. Seoane +9 more
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Counting hypercubes in hypercubes
Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Antipodal Edge-Colorings of Hypercubes
Discussiones Mathematicae Graph Theory, 2019 Two vertices of the k-dimensional hypercube Qkare antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is antipodal to y.
West Douglas B., Wise Jennifer I.
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Path coverings with prescribed ends in faulty hypercubes [PDF]
, 2013 We discuss the existence of vertex disjoint path coverings with prescribed ends for the $n$-dimensional hypercube with or without deleted vertices. Depending on the type of the set of deleted vertices and desired properties of the path coverings we ...
Castañeda, Nelson, Gotchev, Ivan S.
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Extended hypercube: a hierarchical interconnection network of hypercubes [PDF]
IEEE Transactions on Parallel and Distributed Systems, 1992 A new interconnection topology-the extended hypercube-consisting of an interconnection network of k-cubes is discussed. The extended hypercube is a hierarchical, expansive, recursive structure with a constant predefined building block. The extended hypercube retains the positive features of the k-cube at different levels of hierarchy and at the same ...
Kumar, Mohan J, Patnaik, LM
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SIAM Journal on Discrete MathematicsA subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = A+A = \{a + b \ | \ a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. We prove that the number of sumsets in $\mathbb{F}_2^n$ is asymptotically $(2^n-1)2^{2^{n-1}}$. Furthermore, we show that the family of sumsets in $\mathbb{F}_2^n$ is almost identical to the family of all ...
Noga Alon, Or Zamir
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On metric dimensions of hypercubes
Ars Mathematica Contemporanea, 2022 The metric (resp. edge metric or mixed metric) dimension of a graph $G$, is the cardinality of the smallest ordered set of vertices that uniquely recognizes all the pairs of distinct vertices (resp. edges, or vertices and edges) of $G$ by using a vector of distances to this set. In this note we show two unexpected results on hypercube graphs. First, we
Aleksander Kelenc +3 more
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Advanced Intelligent Discovery, EarlyView.This perspective highlights how knowledge‐guided artificial intelligence can address key challenges in manufacturing inverse design, including high‐dimensional search spaces, limited data, and process constraints. It focused on three complementary pillars—expert‐guided problem definition, physics‐informed machine learning, and large language model ...
Hugon Lee +3 more
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A general analytical model of adaptive wormhole routing in k-ary n-cubes [PDF]
, 2003 Several analytical models of fully adaptive routing have recently been proposed for k-ary n-cubes and hypercube networks under the uniform traffic pattern.
Ferguson, J.D. +2 more
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