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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
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
The Turn Model for Adaptive Routing
 JOURNAL OF ACM
, 1994
"... This paper presents a model for designing wormhole routing algorithms, A unique feature of the model is th~t lt is not based cm adding physical or virtual channels to direct networks (although it can be applied to networks with extra channels). Instead, the model is based [In analyzlng the directio ..."
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Cited by 361 (6 self)
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topologies for wormhole routing, ~zdimensional meshes and kary /zcubes without extra channels. In such networks, just a quarter of the turns must be prohibited to prevent deadlock. The remaining three quarters of the turns allow routing to be fidaptwe, Adaptive routing algorithms are described for twodimensional
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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Hamming distance from a, is strictly bigger than ki for all 1 5 i 5 k. The ndimensional cube is the graph whose vertices are all 2 ” binary vectors of length n, in which two vertices are adjacent if and only if their Hamming distance is 1, i.e., they differ in precisely one coordinate. Suppose
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
, 1998
"... We address the problem of designing data structures that allow efficient search for approximate nearest neighbors. More specifically, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a spaceefficient data structure that would allow us to ..."
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Cited by 215 (9 self)
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to search, given a query vector, for the closest or nearly closest vector in the database. We also address this problem when distances are measured by the L 1 norm, and in the Hamming cube. Significantly improving and extending recent results of Kleinberg, we construct data structures whose size
A Lower Bound on the Complexity of Approximate NearestNeighbor Searching on the Hamming Cube
 In Proc. 31th Annual ACM Symposium on Theory of Computing (STOC’99
, 1999
"... We consider the nearestneighbor problem over the dcube: given a collection of points in {0, 1} d , find the one nearest to a query point (in the L 1 sense). We establish a lower bound of###90 log d/ log log log d) on the worstcase query time. This result holds in the cell probe model with ( ..."
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Cited by 19 (3 self)
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We consider the nearestneighbor problem over the dcube: given a collection of points in {0, 1} d , find the one nearest to a query point (in the L 1 sense). We establish a lower bound of###90 log d/ log log log d) on the worstcase query time. This result holds in the cell probe model
On homomorphisms from the Hamming cube to Z
 Israel J. Math
"... Write F for the set of homomorphisms from {0, 1} d to Z which send 0 to 0 (think of members of F as labellings of {0, 1} d in which adjacent strings get labels differing by exactly 1), and Fi for those which take on exactly i values. We give asymptotic formulae for F  and Fi. In particular, we s ..."
Approximate Computation of Multidimensional Aggregates of Sparse Data Using Wavelets
"... Computing multidimensional aggregates in high dimensions is a performance bottleneck for many OLAP applications. Obtaining the exact answer to an aggregation query can be prohibitively expensive in terms of time and/or storage space in a data warehouse environment. It is advantageous to have fast, a ..."
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Cited by 198 (3 self)
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, approximate answers to OLAP aggregation queries. In this paper, we present anovel method that provides approximate answers to highdimensional OLAP aggregation queries in massive sparse data sets in a timeefficient and spaceefficient manner. We construct a compact data cube, which is an approximate
Earth Mover Distance over HighDimensional Spaces
, 2007
"... The Earth Mover Distance (EMD) between two equalsize sets of points in R d is defined to be the minimum cost of a bipartite matching between the two pointsets. It is a natural metric for comparing sets of features, and as such, it has received significant interest in computer vision. Motivated by re ..."
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Cited by 22 (8 self)
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Hamming cube into ℓ1 must incur a distortion Ω(d), thus practically losing all distance information. We circumvent this roadblock by focusing on sets with cardinalities upperbounded by a parameter s, and achieve a distortion of only O(log s · log d). Since in applications the feature sets have bounded
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