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• W2068988049 abstract "A focus of research for crossbar switches has been to reduce the number of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> switch elements, each of which not only occupies a relatively large area but also costs a lot when implemented with optical devices. We point out that conventional <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math> crossbar switches, where <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math> is the switch size, actually function as <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:mo>×</mml:mo><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow></mml:math> switches and thus have redundant <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> switch elements to be removed. We show that ILLIAC<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mo stretchy=false>(</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:math> torus networks, which have a less number of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> switching elements than crossbar switches of an identical switch size, are equivalent to true <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:mi>N</mml:mi><mml:mo>×</mml:mo><mml:mi>N</mml:mi></mml:mrow></mml:math> crossbar switches. We describe in detail how the crossbar switches can be embedded into the equivalent torus networks. We also discuss switch control complexity of the equivalent torus networks and show that it can be reduced to <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mrow><mml:mi>O</mml:mi></mml:mrow></mml:math>(1)." @default.
• W2068988049 created "2016-06-24" @default.
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• W2068988049 date "2012-11-20" @default.
• W2068988049 modified "2023-10-17" @default.
• W2068988049 title "Embedding N × N Crossbar Switches into ILLIAC(N, N − 1) Torus Networks for Optical Interconnection Networks" @default.
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• W2068988049 doi "https://doi.org/10.5402/2012/218541" @default.
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