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hypercube

## hypercube

```  1  definition  found

From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]:

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}.

(1994-11-17)

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