On the topological properties of grid-based interconnection networks: Surface area and volume of radial spheres

H. Sarbazi-Azad, A. Khonsari, M. Ould-Khaoua

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4 Citations (Scopus)


Grid-based networks (or grids for short), such as meshes and tori, have been the underlying topology for many multicomputers, and have been extensively studied in the past as a graph topology. In this paper, we investigate some topological properties of grids without boundary wrap-around (meshes) and with boundary wrap-around (tori). In particular, we study the problem of finding the number of nodes located at/within a given distance from a given node (surface area/volume) in the network and derive some expressions for computing such a number. Furthermore, we provide similar expressions that improve on previous results already reported in the literature for some special cases of grids, notably hypercubes and k-ary n-cubes. We also show some applications of the derived expressions in analytical performance modelling of some grid-based networks under uniform and hotspot traffic loads.

Original languageEnglish
Pages (from-to)726-737
Number of pages12
JournalComputer Journal
Issue number5
Publication statusPublished - May 2011



  • combinatorial properties
  • hypercubes
  • interconnection networks
  • k-ary n-cubes
  • meshes
  • multicomputers
  • topology
  • tori

ASJC Scopus subject areas

  • Computer Science(all)

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