Annals of Combinatorics 2 (1998) 165-172


Fault-tolerant Routing in Circulant Networks and Cycle Prefix networks

Sheng-Chyang Liaw1, Gerard J. Chang1, Feng Cao2, and D. Frank Hsu3

1Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan
  {scliaw, gjchang}@math.nctu.edu.tw

2Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, USA
  cao@cs.umn.edu

3Department of Computer and Information Science, Fordham University   LL813, 113 West 60th Street, New York, NY 10023, USA
  hsu@murray.fordham.edu

Received October 22, 1996

AMS Subject Classification: 05C12, 05C40

Abstract. Reliability and efficiency are important criteria in the design of interconnection networks. Connectivity is a widely used measurement for network fault-tolerance capacities, while diameter determines routing efficiency along individual paths. In practice, we are interested in high-connectivity, small-diameter networks. Recently, Hsu introduced the notion of w-wide diameter, which unifies diameter and connectivity. This paper investigates the w-wide diameter dw(G) and two related parameters: w-fault diameter Dw(G) and w-Rabin number rw(G). In particular, we determine dw(G) and Dw(G) for $2 \le w \le k(G)$ and G is a circulant digraph G(dn; {1,d,...,dn-1}) or a cycle prefix digraph.

Keywords: routing, circulant network, cycle prefix network, connectivity, diameter, container, wide diameter, fault diameter, Rabin number


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