# 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 ?
The expanded k-ary n-cube, denoted by X[Q.sup.k.sub.n] (n [greater than or equal to] 1 and even k [greater than or equal to] 6), is a graph consisting of [k.sup.n] vertices {[u.sub.0][u.sub.1] ...
The expanded k-ary n-cube is the Cartesian product of n expanded k-ary 1-cubes, i.e., [mathematical expression not reproducible].
Guy, "The crossing number of the n-cube," Notices of the American Mathematical Society, vol.
Figure 2 demonstrates how the hyperplane (line), which is the line of a constant sum of the values of the random variables and is perpendicular to the n-cube's (square's) main diagonal, accrues volume (area) below it.
From Example 3.10, we see that the n-cube and the folded n-cube can be quotients of H(n, 4).
In other words an n-cube is a connected graph of diameter n.
Hypercubes are special cases of an n-dimensional mesh in which [k.sub.i] = 2, for all i, 0 [is less than or equal to] i [is less than or equal to] n - 1; they can be termed 2-ary n-cubes. A k-ary n-cube is called a torus when n = 2.
Hypercubes, i.e., binary n-cube interconnection systems, have been extensively studied in recent years [Chiu et al.
This dispute originated in 2001, when n-Cube Corporation (whose interest was later acquired by Arris Group) filed suit alleging that SeaChange's ITV video system infringed an n-Cube patent.
Multistage networks of different types have been shown to be topologically equivalent  and we shall consider here as a representative of this class, the indirect binary n-cube network .
Four multiprocessing systems participated: PHOENIX used 20 SUN-3 workstations located at SUN Microsystems, in mountain View, Calif., FIDELITY EXPERIMENTAL used 28 6502's and one Z-80, OSTRICH ran on an 8-processor Data General system, and WAYCOOL, a new program developed at Cal Tech, used a 128-processor N-cube. Three programs, BELLE, BEBE, AND CHIPTEST, took advantage of specially designed circuitry that generated moves and scored positions at high speeds.

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