IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Special Section on Multiple-Valued Logic and VLSI Computing
Realization of Multi-Terminal Universal Interconnection Networks Using Contact Switches
Tsutomu SASAOTakashi MATSUBARAKatsufumi TSUJIYoshiaki KOGA
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2021 Volume E104.D Issue 8 Pages 1068-1075

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Abstract

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.

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© 2021 The Institute of Electronics, Information and Communication Engineers
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