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hypercube
hy·per·cube H5378000 (hī′pər-kyo͞ob′)n.1. Any of a set of objects resulting from the generalization of a two-dimensional square and a three-dimensional cube to n dimensions. A hypercube has 2n corners, each of which is connected to its n nearest adjacent corners by edges that all have the same length.2. A network whose nodes have the connectivity of such an object.hypercube (ˈhaɪpəˌkjuːb) n (Mathematics) maths a figure in a space of four or more dimensions having all its sides equal and all its angles right angleshypercube
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). hypercubeA cube of more than three dimensions. A single (2^0 = 1)point (or "node") can be considered as a zero dimensionalcube, two (2^1) nodes joined by a line (or "edge") are a onedimensional cube, four (2^2) nodes arranged in a square are atwo dimensional cube and eight (2^3) nodes are an ordinarythree dimensional cube. Continuing this geometricprogression, the first hypercube has 2^4 = 16 nodes and is afour dimensional shape (a "four-cube") and an N dimensionalcube has 2^N nodes (an "N-cube"). To make an N+1 dimensionalcube, take two N dimensional cubes and join each node on onecube to the corresponding node on the other. A four-cube canbe visualised as a three-cube with a smaller three-cubecentred inside it with edges radiating diagonally out (in thefourth dimension) from each node on the inner cube to thecorresponding node on the outer cube.
Each node in an N dimensional cube is directly connected to Nother nodes. We can identify each node by a set of NCartesian coordinates where each coordinate is either zeroor one. Two node will be directly connected if they differ inonly one coordinate.
The simple, regular geometrical structure and the closerelationship between the coordinate system and binary numbersmake the hypercube an appropriate topology for a parallelcomputer interconnection network. The fact that the number ofdirectly connected, "nearest neighbour", nodes increases withthe total size of the network is also highly desirable for aparallel computer.hypercubeA 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.MedicalSeetopology |