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Static Connection Networks

See additional Figures.

• k-ary n-cube networks: dimension k, N=n^k nodes.
  • Line/ring (1D), mesh/torus (2D), cube (3D).
  • Degree: 2^k = const.
  • Diameter: k(n-1) = ksqrt [k]N.
  • Bisection width: n^k-1.
  • Edge length: constant.
• Hypercube: binary n-cube, N=2ⁿ.
  • Degree: n (not constant).
  • Diameter: n=log ₂ N.
  • Bisection width: 2k^k-1.
  • Edge length: not constant.
  • Scalability only by factors of 2!

Today, low-dimensional (2D, 3D) meshes are preferred over hypercubes.