hypercube

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hypercube

[′hī·pər ‚kyüb]
(computer science)
A configuration of parallel processors in which the locations of the processors correspond to the vertices of a mathematical hypercube and the links between them correspond to its edges.
(mathematics)
The analog of a cube in n dimensions (n = 2, 3, ….), with 2 n vertices, n 2 n-1edges, and 2 n cells; for an object with edges of length 2 a, the coordinates of the vertices are (± a, ± a, …, ± a).

hypercube

A cube of more than three dimensions. A single (2^0 = 1) point (or "node") can be considered as a zero dimensional cube, two (2^1) nodes joined by a line (or "edge") are a one dimensional cube, four (2^2) nodes arranged in a square are a two dimensional cube and eight (2^3) nodes are an ordinary three dimensional cube. Continuing this geometric progression, the first hypercube has 2^4 = 16 nodes and is a four dimensional shape (a "four-cube") and an N dimensional cube has 2^N nodes (an "N-cube"). To make an N+1 dimensional cube, take two N dimensional cubes and join each node on one cube to the corresponding node on the other. A four-cube can be visualised as a three-cube with a smaller three-cube centred inside it with edges radiating diagonally out (in the fourth dimension) from each node on the inner cube to the corresponding node on the outer cube.

Each node in an N dimensional cube is directly connected to N other nodes. We can identify each node by a set of N Cartesian coordinates where each coordinate is either zero or one. Two node will be directly connected if they differ in only one coordinate.

The simple, regular geometrical structure and the close relationship between the coordinate system and binary numbers make the hypercube an appropriate topology for a parallel computer interconnection network. The fact that the number of directly connected, "nearest neighbour", nodes increases with the total size of the network is also highly desirable for a parallel computer.

hypercube

A parallel processing architecture made up of binary multiples of computers (4, 8, 16, etc.). The computers are interconnected so that data travel is kept to a minimum. For example, in two eight-node cubes, each node in one cube would be connected to the counterpart node in the other.
References in periodicals archive ?
5] Adrian Enache, Costin Boiangiu, A Pyramidal Scheme of Residue Hypercubes for Adaptive Video Streaming, International Journal of Computers and Communications, volume 8, pp.
The following properties of hypercubes shall be useful later.
7 Sparse regular spanning subgraphs of the hypercubes with the PH-property.
It starts with a single driving strategy with empty hypercubes.
Lastly, the relationships all and not-all state, for a given fact, whether all domain members are part of the hypercube or not.
The structure is abstracted into three tiers: mobile node (MN), hypercube tier (HT) and mesh tier (MT).
Topics include object serialization in Java remote method invocation, data clustering of tolerance space in Matlab, genetic algorithms for hunting snakes in hypercubes, a web-based cooperative research paper edit system, and text classification by combining different distance functions with weights.
In this way the entire search space is divided into 2dk unique equal size k--dimensional hypercubes (d is a user parameter and k is the number of objective functions).
We note that queries using the maximum metric correspond to hypercubes rather than hyperspheres.
Hypercubes are special cases of an n-dimensional mesh in which [k.
They include computations of the star discrepancy (a measure of nonuniformity based on hypercubes that include the origin - see Hickernell [1995], Niederreiter [1992], or Sloan and Joe [1994]) and computations of the error of the quasi Monte Carlo integration.

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