IEICE TRANSACTIONS on Information
Realization of Multi-Terminal Universal Interconnection Networks Using Contact Switches
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
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Tsutomu SASAO, Takashi MATSUBARA, Katsufumi TSUJI, Yoshiaki KOGA, "Realization of Multi-Terminal Universal Interconnection Networks Using Contact Switches" in IEICE TRANSACTIONS on Information,
vol. E104-D, no. 8, pp. 1068-1075, August 2021, doi: 10.1587/transinf.2020LOP0001.
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 $ 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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2020LOP0001/_p
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@ARTICLE{e104-d_8_1068,
author={Tsutomu SASAO, Takashi MATSUBARA, Katsufumi TSUJI, Yoshiaki KOGA, },
journal={IEICE TRANSACTIONS on Information},
title={Realization of Multi-Terminal Universal Interconnection Networks Using Contact Switches},
year={2021},
volume={E104-D},
number={8},
pages={1068-1075},
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 $ 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.},
keywords={},
doi={10.1587/transinf.2020LOP0001},
ISSN={1745-1361},
month={August},}
Copy
TY - JOUR
TI - Realization of Multi-Terminal Universal Interconnection Networks Using Contact Switches
T2 - IEICE TRANSACTIONS on Information
SP - 1068
EP - 1075
AU - Tsutomu SASAO
AU - Takashi MATSUBARA
AU - Katsufumi TSUJI
AU - Yoshiaki KOGA
PY - 2021
DO - 10.1587/transinf.2020LOP0001
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E104-D
IS - 8
JA - IEICE TRANSACTIONS on Information
Y1 - August 2021
AB - 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.
ER -
English
