Construction of large-size interconnection networks with high performance

Hong Shen, Ralph Johan Back

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper proposes a new method, recursive expansion (RE), for systematically constructing interconnection networks of arbitrary large size with high performance. On the basis of two small-size networks, a frame and a unit, the RE method works in a manner of recursively replacing each node in the frame with an expanded network containing a set of copies of the unit and each edge in the frame with a set of inter-unit connections connecting a pair of the networks until a network of the desired size has been obtained. By RE, we can construct various kinds of large-size and low-cost interconnection networks. Two applications of the method TrΣ-network based on the torus and the HrΣ-network based on the hypercube, show that our method can produce networks with cost O( log 3 2 n log 3 2 log n) (degree O(1)) and O(log n log log n) (degree O(log log n). In addition to low cost, networks constructed by RE also possess other properties such as high constructability, good extendability symmetric topology and efficient message routing. Based on the RE method, this paper consequently describes an algorithm for automatically constructing arbitrary large-size networks with high performance. For constructing a network of size nr through r phases RE on the basis of a frame of degree dl and a unit of size nu and degree du, the algorithm has a time complexity O((max { df nU, dr rU})rnr2). Finally, a routing algorithm for networks constructed by RE is presented. The routing algorithm can realize point-to-point message routing without using a global routing table at each node and has a time complexity O((ku + kf)dfr), where ku and kf are diameters of the frame and of the unit, df is the degree of the frame, and r is the number of phases of RE to construct the network.

Original languageEnglish
Pages (from-to)545-554
Number of pages10
JournalMicroprocessing and Microprogramming
Issue number1-5
Publication statusPublished - Sept 1992
Externally publishedYes


  • Interconnection network
  • cost
  • degree
  • diameter
  • message routing
  • performance
  • recursive expansion
  • size


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