On a Realization of Multi-terminal Universal Interconnection Networks using Contact Switches

Abstract

A universal interconnection network implements ar-bitrary interconnections among n terminals. This paper considers a problem to realize such a network using contact switches. When n = 2, it can be implemented with a single switch. The number of different connections among n terminals is given by the Bell number B(n). The Bell number shows the total number of methods to partition n distinct elements. For n = 2, 3, 4, 5 and 6, the corresponding Bell numbers are 2, 5, 15, 52, and 203, respectively. This paper shows a method to realize an n terminal universal interconnection network with $\frac{3}{8}\left( {{n^2} - 1} \right)$ contact switches when n = 2m + 1 ≥ 5, and $\frac{n}{8}(3n + 2)$ contact switches, when n = 2m ≥ 6. Also, it shows a lower bound on the number of contact switches to realize an n-terminal universal interconnection network.