Realization of Multi-Terminal Universal Interconnection Networks Using Contact Switches

摘要

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 $rac {3}{8}(n^2-1)$ contact switches when n =2m +1≥5, and $rac {n}{8}(3n+2)$ 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 _(2)B (n )?, where B (n ) is the Bell number.