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 "fourcube") and an N dimensional cube
has 2^N nodes (an "Ncube"). 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 fourcube can be visualised as a threecube with a smaller
threecube 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.
(19941117)
Nearby terms:
HyperBase « HyperC « HyperCard « hypercube »
Hyperion » hyperlink » HyperMan
