2021 年 E104.D 巻 8 号 p. 1068-1075
A universal interconnection network implements arbitrary 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 $\frac {3}{8}(n^2-1)$ contact switches when n=2m+1≥5, and $\frac {n}{8}(3n+2)$ contact switches, when n=2m≥6. Also, it shows that a lower bound on the number of contact switches to realize an n-terminal universal interconnection network is ⌈log 2B(n)⌉, where B(n) is the Bell number.
