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 2ⁿvertices, 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.

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References in periodicals archive ?

The conclusion will be that a network such as a hypercube will suffice for optimality to within constant factors, but only if its communication bandwidth is balanced with its computational capability.

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In this paper, we propose another variant of Radviz that supports users visualizing the data inside a hypercube from an arbitrary viewpoint at the corners of the hypercube.

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A 25 point optimal Latin hypercube DoE is constructed using the approach described earlier.

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Keywords: Gray code, Hamiltonian cycle, hypercube, long cycle, matching, Ruskey and Savage problem

Matchings of quadratic size extend to long cycles in hypercubes

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We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d [greater than or equal to] 7 and every k, where 7 [less than or equal to] k [less than or equal to] d, the d-dimensional hypercube contains a k-regular spanning subgraph such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle.

Extending a perfect matching to a Hamiltonian cycle

In this paper, we aim to design efficient multicast routing schemes in data center networks which are based on the concept of generalized hypercube, such as BCube, FBFLY, and HyperX.

Efficient multicast routing on BCube-based data centers

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Uncertainty analysis for large-scale prediction of the van Genuchten soil-water retention parameters with pedotransfer functions