# 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 ?
10, we see that the n-cube and the folded n-cube can be quotients of H(n, 4).
But when n is even, the n-cube admits a second Q-polynomial structure, with eigenvalue ordering
We are pleased the Court has recognized that SeaChange took appropriate steps after the 2001 litigation with n-Cube, and that SeaChange has at all times complied with the Court s Order, said SeaChange General Counsel David McEvoy.
The nodes of an n-cube are represented by n-bit binary addresses.
Here we classify fully adaptive routing algorithms on the basis of the number of VCs required per physical channel (PC) for a k-ary n-cube network.
binary n-cube interconnection systems, have been extensively studied in recent years [Chiu et al.
As an example of application of the ideas developed in this article to other popular networks, we outline an improved routing algorithm for the k-ary n-cube interconnection network in the following subsection.
However, seven years later, in 2009, Arris filed a motion alleging that SeaChange's 2002 work-around violated the injunction from the n-Cube case.
The direct binary n-cube or hypercube network  consist of [N = 2.

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