A cube of more than three dimen
sion
s. A
single (2^0 = 1) point (or "node") can be con
sidered a
s a zero dimen
sional cube, two (2^1) node
s joined by a line (or "edge") are a one dimen
sional cube, four (2^2) node
s arranged in a
square are a two dimen
sional cube and eight (2^3) node
s are an ordinary three dimen
sional cube. Continuing thi
s geometric progre
ssion, the fir
st hypercube ha
s 2^4 = 16 node
s and i
s a four dimen
sional
shape (a "four-cube") and an N dimen
sional cube ha
s 2^N node
s (an "N-cube"). To make an N+1 dimen
sional cube, take two N dimen
sional cube
s and join each node on one cube to the corre
sponding node on the other. A four-cube can be vi
suali
sed a
s a three-cube with a
smaller three-cube centred in
side it with edge
s radiating diagonally out (in the fourth dimen
sion) from each node on the inner cube to the corre
sponding node on the outer cube. Each node in an N dimen
sional cube i
s directly connected to N other node
s. We can identify each node by a
set of N
Cartesian coordinates where each coordinate i
s either zero or one. Two node will be directly connected if they differ in only one coordinate. The
simple, regular geometrical
structure and the clo
se relation
ship between the coordinate
sy
stem and binary number
s make the hypercube an appropriate topology for a parallel computer interconnection network. The fact that the number of directly connected, "neare
st neighbour", node
s increa
se
s with the total
size of the network i
s al
so highly de
sirable for a
parallel computer. (1994-11-17)
style="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
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