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Realization of Multi-Terminal Universal Interconnection Networks Using Contact Switches

Tsutomu SASAO, Takashi MATSUBARA, Katsufumi TSUJI, Yoshiaki KOGA

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Summary :

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 2B(n)⌉, where B(n) is the Bell number.

Publication
IEICE TRANSACTIONS on Information Vol.E104-D No.8 pp.1068-1075
Publication Date
2021/08/01
Publicized
2021/04/01
Online ISSN
1745-1361
DOI
10.1587/transinf.2020LOP0001
Type of Manuscript
Special Section PAPER (Special Section on Multiple-Valued Logic and VLSI Computing)
Category
Logic Design

Authors

Tsutomu SASAO
  Meiji University
Takashi MATSUBARA
  National Defence Academy
Katsufumi TSUJI
  Fujitsu Limited
Yoshiaki KOGA
  National Defence Academy

Keyword