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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)