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511
Transmitting in the ndimensional cube
 Discrete Applied Mathematics
, 1992
"... Alon, N., Transmitting in the ndimensional cube, Discrete Applied Mathematics 37/38 (1992) 91 I. Motivated by a certain communication problem we show that for any integer n and for any sequence (a,,...,ak) of k = [n/21 binary vectors of length n, there is a binary vector z of length n whose Hammin ..."
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Cited by 4 (0 self)
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Alon, N., Transmitting in the ndimensional cube, Discrete Applied Mathematics 37/38 (1992) 91 I. Motivated by a certain communication problem we show that for any integer n and for any sequence (a,,...,ak) of k = [n/21 binary vectors of length n, there is a binary vector z of length n whose
Data cube: A relational aggregation operator generalizing groupby, crosstab, and subtotals
, 1996
"... Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zerodimensional or onedimensional aggregates. Applications need the Ndimensional generalization of these op ..."
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Cited by 860 (11 self)
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in more complex nonprocedural data analysis programs. The cube operator treats each of the N aggregation attributes as a dimension of Nspace. The aggregate of a particular set of attribute values is a point in this space. The set of points forms an Ndimensional cube. Superaggregates are computed
On the Eggleton and Guy conjectured upper bound for the crossing number of the ncube
 MATH. SLOVACA
, 1997
"... Let Q n denote the ndimensional cube. In this paper, we exhibit drawings for n = 6, 7 and 8. In these cases the drawings confirm Eggleton and Guy's conjectured upper bound for the crossing number of the ncube. ..."
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Cited by 6 (1 self)
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Let Q n denote the ndimensional cube. In this paper, we exhibit drawings for n = 6, 7 and 8. In these cases the drawings confirm Eggleton and Guy's conjectured upper bound for the crossing number of the ncube.
JOURNAL OF COMBINATORIAL THEORY (A) 20, 170177 (1976) Triangulations for the Cube
, 1975
"... In this note we consider the problem of determining a minimal triangulation of I”, the ndimensional cube. While the problem seems intrinsically interesting, our purpose in presenting it is motivated by the interest evinced in connection with the simplicial approximation of fixed points of ..."
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In this note we consider the problem of determining a minimal triangulation of I”, the ndimensional cube. While the problem seems intrinsically interesting, our purpose in presenting it is motivated by the interest evinced in connection with the simplicial approximation of fixed points of
The cyclic cutwidth of Qn
, 2003
"... In this article the cyclic cutwidth of the ndimensional cube is explored. It has been conjectured by Dr. Chavez and Dr. Trapp that the cyclic cutwidth of Qn is minimized with the Greycode numbering. Several results have been found toward the proof of this conjecture. ..."
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In this article the cyclic cutwidth of the ndimensional cube is explored. It has been conjectured by Dr. Chavez and Dr. Trapp that the cyclic cutwidth of Qn is minimized with the Greycode numbering. Several results have been found toward the proof of this conjecture.
The FirstPassage Diameter of the the Cube
, 2000
"... We show that if the edges of the ndimensional cube are assigned independent weights chosen uniformly from [0; 1] then with probability tending to 1 every pair of vertices is connected by a path of total weight at most a constant. A similar result holds when the uniform distribution is replaced by a ..."
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We show that if the edges of the ndimensional cube are assigned independent weights chosen uniformly from [0; 1] then with probability tending to 1 every pair of vertices is connected by a path of total weight at most a constant. A similar result holds when the uniform distribution is replaced
Some Ramsey results for the ncube
"... In this note we establish a Ramseytype result for certain subsets of the ndimensional cube. This can then be applied to obtain reasonable bounds on various related structures, such as (partial) HalesJewett lines for alphabets of sizes 3 and 4, Hilbert cubes in sets of real numbers with small sums ..."
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Cited by 1 (1 self)
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In this note we establish a Ramseytype result for certain subsets of the ndimensional cube. This can then be applied to obtain reasonable bounds on various related structures, such as (partial) HalesJewett lines for alphabets of sizes 3 and 4, Hilbert cubes in sets of real numbers with small
Performance analysis of kary ncube interconnection networks
 IEEE Transactions on Computers
, 1990
"... AbstmctVLSI communication networks are wirelimited. The cost of a network is not a function of the number of switches required, but rather a function of the wiring density required to construct the network. This paper analyzes communication networks of varying dimension under the assumption of co ..."
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Cited by 357 (18 self)
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of constant wire bisection. Expressions for the latency, average case throughput, and hotspot throughput of kary ncube networks with constant bisection are derived that agree closely with experimental measurements. It is shown that lowdimensional networks (e.g., tori) have lower latency and higher hot
Results 1  10
of
511