A simple algorithm to find the steps of double-loop networks

  • Authors:

  • Robin Chi-Feng Chan;Chiuyuan Chen;Zhi-Xin Hong

  • Affiliations:

  • Department of Applied Mathematics, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300, Taiwan;Department of Applied Mathematics, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300, Taiwan;Department of Applied Mathematics, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 300, Taiwan

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2002

Quantified Score

Hi-index 0.05

Visualization

Abstract

Double-loop networks have been widely studied as architecture for local area networks and it is well-known that the minimum distance diagram of a double-loop network yields an L-shape. Given an N, it is desirable to find a double-loop network DL(N; s1, s2) with its diameter being the minimum among all double-loop networks with N stations. Since the diameter can be easily computed from an L-shape, one method is to start with a desirable L-shape and then asks whether there exist s1 and s2 (also called the steps of the double-loop network) to realize it. In this paper, we propose a simple and efficient algorithm to find s1 and s2, which is based on the Smith normalization method of Aguiló, Esqué and Fiol.