## Abstract

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 T_{r}^{Σ}-network based on the torus and the H_{r}^{Σ}-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 n_{r} through r phases RE on the basis of a frame of degree d_{l} and a unit of size n_{u} and degree d_{u}, the algorithm has a time complexity O((max { d_{f} n_{U}, d_{r} r_{U}})rn_{r}^{2}). 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((k_{u} + k_{f})d_{fr}), where k_{u} and k_{f} are diameters of the frame and of the unit, d_{f} is the degree of the frame, and r is the number of phases of RE to construct the network.

Original language | English |
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Pages (from-to) | 545-554 |

Number of pages | 10 |

Journal | Microprocessing and Microprogramming |

Volume | 35 |

Issue number | 1-5 |

DOIs | |

Publication status | Published - Sept 1992 |

Externally published | Yes |

## Keywords

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