M—0041 US
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`FULLY CONNECTED GENERALIZED FOLDED MULTI-STAGE NETWORKS
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`Venkat Konda
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`5
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`CROSS REFERENCE TO RELATED APPLICATIONS
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M—0037US entitled "FULLY CONNECTED
`
`GENERALIZED MULTI-STAGE NETWORKS" by Venkat Konda assigned to the same
`
`assignee as the current application, filed concurrently.
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`10
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`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M-003 SUS entitled ”FULLY CONNECTED
`
`GENERALIZED BUTTERFLY FAT TREE NETWORKS" by Venkat Konda assigned
`
`to the same assignee as the current application, filed concurrently.
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`15
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`Provisional Patent Application Docket No. M—0039US entitled "FULLY CONNECTED
`
`GENERALIZED REARRANGEABLY NONBLOCKING MULTI-LINK MULTI-
`
`STAGE NETWORKS" by Venkat Konda assigned to the same assignee as the current
`
`application, filed concurrently.
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`This application is related to and incorporates by reference in its entirety the U.S.
`
`20
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`Provisional Patent Application Docket No. M-0040US entitled "FULLY CONNECTED
`
`GENERALIZED MULTI-LINK BUTTERFLY FAT TREE NETWORKS" by Venkat
`
`Konda assigned to the same assignee as the current application, filed concurrently.
`
`This application is related to and incorporates by reference in its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0042US entitled "FULLY CONNECTED
`
`25
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`GENERALIZED STRICTLY NONBLOCKING MULTI—LINK MULTI-STAGE
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`NETWORKS" by Venkat Konda assigned to the same assignee as the current application,
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`filed concurrently.
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`FLEX LOGIX EXHIBIT 1022
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`FLEX LOGIX EXHIBIT 1022
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`M—0041 US
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`This application is related to and incorporates by reference in its entirety the US
`
`Provisional Patent Application Docket No. M-0045US entitled ”VLSI LAYOUTS OF
`
`FULLY CONNECTED GENERALIZED NETWORKS" by Venkat Konda assigned to
`
`the same assignee as the current application, filed concurrently.
`
`BRIEF DESCRIPTION OF DRAWINGS
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`FIG. 1A is a diagram 100A of an exemplary symmetrical folded multi-stage
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`network Vfold (N,d , s) having inverse Benes connection topology of five stages with N =
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`8, d = 2 and s=2 with exemplary multicast connections, strictly nonblocking network for
`
`unicast connections and rearrangeably nonblocking network for arbitrary fan-out
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`multicast connections, in accordance with the invention.
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`FIG. 1A1 is a diagram 100A1 of an exemplary symmetrical folded multi-stage
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`network anm (N ,d ,2) having Omega connection topology of five stages with N = 8, d =
`
`2 and s=2 with exemplary multicast connections, strictly nonblocking network for unicast
`
`connections and rearrangeably nonblocking network for arbitrary fan-out multicast
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`connections, in accordance with the invention.
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`FIG. 1A2 is a diagram 100A2 of an exemplary symmetrical folded multi-stage
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`network Vfold (N ,d ,2) having nearest neighbor connection topology of five stages with N
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`= 8, d = 2 and s=2 with exemplary multicast connections, strictly nonblocking network
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`for unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`FIG. 1B is a diagram 100B of a general symmetrical folded multi-stage network
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`V/UM (N,d,2) with (2Xlog d N )—1
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`stages strictly nonblocking network for unicast
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`connections and rearrangeably nonblocking network for arbitrary fan-out multicast
`
`connections in accordance with the invention.
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`FlG. 1C is a diagram 100C of an exemplary asymmetrical folded multi-stage
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`network Vfold (N1, N2,d ,2) having inverse Benes connection topology of five stages with
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`N1 = 8, N2 = p* N1 = 24 where p = 3, and d = 2 with exemplary multicast connections,
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`strictly nonblocking network for unicast connections and rearrangeably nonblocking
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`network for arbitrary fan-out multicast connections, in accordance with the invention.
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`FIG. 1C1 is a diagram 100C1 of an exemplary asymmetrical folded multi-stage
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`network Vfold (N1,N2,d ,2) having Omega connection topology of five stages with N1 =
`
`8, N2 = p* N1 = 24 where p = 3, and d = 2 with exemplary multicast connections, strictly
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`nonblocking network for unicast connections and rearrangeably nonblocking network for
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`arbitrary fan-out multicast connections, in accordance with the invention.
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`FIG. 1C2 is a diagram 100C2 of an exemplary asymmetrical folded multi-stage
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`network VIM (N1,N2,d ,2) having nearest neighbor connection topology of five stages
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`with N1 = 8, N2 = p* N1 = 24 where p = 3, and d = 2 with exemplary multicast
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`connections, strictly nonblocking network for unicast connections and rearrangeably
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`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
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`FIG. 1D is a diagram 100D of a general asymmetrical folded multi-stage network
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`Vfold (N1,N2,d,2) with N2 = p* N1 and with (2Xlogd N)—1 stages strictly nonblocking
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`network for unicast connections and rearrangeably nonblocking network for arbitrary fan-
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`out multicast connections in accordance with the invention.
`
`FIG. 1B is a diagram 100E of an exemplary asymmetrical folded multi-stage
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`network Vfold (N1, N2,d ,2) having inverse Benes connection topology of five stages with
`
`N2 = 8, N1 = p* N2 = 24, where p = 3, and d = 2 with exemplary multicast connections,
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`strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`network for arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 1E1 is a diagram 100E1 of an exemplary asymmetrical folded multi-stage
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`network anm (N1 ,N2,d ,2) having Omega connection topology of five stages with N2 =
`
`8, N1 = p* N2 = 24, where p = 3, and d = 2 with exemplary multicast connections,
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`strictly nonblocking network for unicast connections and rearrangeably nonblocking
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`network for arbitrary fan-out multicast connections, in accordance with the invention.
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`FIG. IE2 is a diagram 100E2 of an exemplary asymmetrical folded multi-stage
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`network Vfold (N1,N2,d ,2) having nearest neighbor connection topology of five stages
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`with N2 = 8, N1 = p* N2 = 24, where p = 3, and d = 2 with exemplary multicast
`
`connections, strictly nonblocking network for unicast connections and rearrangeably
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
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`FIG. 1F is a diagram 100F of a general asymmetrical folded multi-stage network
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`Vfold (N1,N2,d,2) with N1 = p* N2 and with (2Xlogd N)—l stages strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking network for arbitrary fan-
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`10
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`out multicast connections in accordance with the invention.
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`FIG. 2A is a diagram 200A of an exemplary symmetrical folded multi-stage
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`network VIM (N,d , 5) having inverse Benes connection topology of five stages with N =
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`8, d = 2 and s=1 with exemplary unicast connections rearrangeably nonblocking network
`
`for unicast connections, in accordance with the invention.
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`FIG. 2B is a diagram 200B of a general symmetrical folded multi-stage network
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`Vfold (N,d ,1) with (2Xlogd N )—1 stages rearrangeably nonblocking network for unicast
`
`connections in accordance with the invention.
`
`FIG. 2C is a diagram 200C of an exemplary asymmetrical folded multi-stage
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`network VIM (N1,N2,d,l) having inverse Benes connection topology of five stages with
`
`N1 = 8, N2 = p* N1 = 24 where p = 3, and d = 2 with exemplary unicast connections
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`rearrangeably nonblocking network for unicast connections,
`
`in accordance with the
`
`invention.
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`FIG. 2D is a diagram 200D of a general asymmetrical folded multi-stage network
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`Vfold(N1,N2,d,l) with N2 = p* N1 and with (2Xlogd N)—l
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`stages rearrangeably
`
`nonblocking network for unicast connections in accordance with the invention.
`
`FIG. 2B is a diagram 200E of an exemplary asymmetrical folded multi-stage
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`network anld (N1,N2,al ,1) having inverse Benes connection topology of five stages with
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`N2 = 8, N1 = p"< N2 = 24, where p = 3, and d = 2 with exemplary unicast connections
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`rearrangeably nonblocking network for unicast connections,
`
`in accordance with the
`
`invention.
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`FIG. 2F is a diagram 200F of a general asymmetrical folded multi-stage network
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`Vf,,d(N1,N,,d,1) with N1
`
`p* N2 and with (2Xlog d N )—1
`
`stages rearrangeably
`
`nonblocking network for unicast connections in accordance with the invention.
`
`FIG. 3A is a diagram 300A of an exemplary symmetrical multi-stage network
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`V(N,d, 5) having inverse Benes connection topology of five stages with N = 8, d = 2 and
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`s = 1, rearrangeably nonblocking network for unicast connections, in accordance with the
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`10
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`invention.
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`FIG. 3B is a diagram 300B of an exemplary symmetrical multi-stage network
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`V(N,d, 5) (having a connection topology built using back-to-back Omega Networks) of
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`five stages with N = 8, d = 2 and s = 1, rearrangeably nonblocking network for unicast
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`connections.
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`FIG. 3C is a diagram 300C of an exemplary symmetrical multi-stage network
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`V(N,d, 3) having an exemplary connection topology of five stages with N = 8, d = 2 and
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`s=1, rearrangeably nonblocking network for unicast connections, in accordance with the
`
`invention.
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`FIG. 3D is a diagram 300D of an exemplary symmetrical multi-stage network
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`V(N,d, s) having an exemplary connection topology of five stages with N = 8, d = 2 and
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`s = 1, rearrangeably nonblocking network for unicast connections, in accordance with the
`
`invention.
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`FIG. 3E is a diagram 300E of an exemplary symmetrical multi—stage network
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`V(N,d, 5) (having a connection topology called flip network and also known as inverse
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`shuffle exchange network) of five stages with N = 8, d = 2 and s = 1, rearrangeably
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`nonblocking network for unicast connections.
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`FIG. 3F is a diagram 300F of an exemplary symmetrical multi-stage network
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`V(N,d, 5) having Baseline connection topology of five stages with N = 8, d = 2 and s =
`
`1, rearrangeably nonblocking network for unicast connections.
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`FIG. 3G is a diagram 300G of an exemplary symmetrical multi-stage network
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`V(N,d, 5) having an exemplary connection topology of five stages with N = 8, d = 2 and
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`s = 1, rearrangeably nonblocking network for unicast connections, in accordance with the
`
`invention.
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`FIG. 3H is a diagram 300H of an exemplary symmetrical multi-stage network
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`V(N,d, 5) having an exemplary connection topology of five stages with N = 8, d = 2 and
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`s = 1, rearrangeably nonblocking network for unicast connections, in accordance with the
`
`invention.
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`FIG. 31 is a diagram 3001 of an exemplary symmetrical multi-stage network
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`V(N,d, 5) (having a connection topology built using back-to-back Banyan Networks or
`
`back-to-back Delta Networks or equivalently back-to-back Butterfly networks) of five
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`stages with N = 8, d = 2 and s = 1, rearrangeably nonblocking network for unicast
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`connections.
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`FIG. 3] is a diagram 300J of an exemplary symmetrical multi-stage network
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`V(N,d, s) having an exemplary connection topology of five stages with N = 8, d = 2 and
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`s = 1, rearrangeably nonblocking network for unicast connections.
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`FIG. 3K is a diagram 300K of a general symmetrical multi—stage network
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`V(N,d, s) with (2Xlogd N )—1 stages with s = 1, rearrangeably nonblocking network for
`
`unicast connections in accordance with the invention.
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`FIG. 3A1 is a diagram 300A1 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,al , s) having inverse Benes connection topology of five stages with N1 = 8, N2
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`= p* N1 = 24 where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast
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`connections, in accordance with the invention.
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`FIG. 3B1 is a diagram 300B1 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d,s)
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`(having a connection topology built using back-to-back Omega
`
`Networks) of five stages with N1 = 8, N2 = p* N1 = 24 where p = 3, d = 2 and s = 1,
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`rearrangeably nonblocking network for unicast connections.
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`FIG. 3C1 is a diagram 300C1 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d,s) having an exemplary connection topology of five stages with N1 = 8, N2
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`= p* N1 = 24 where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast
`
`connections, in accordance with the invention.
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`10
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`FIG. 3D] is a diagram 300D] of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d ,5) having an exemplary connection topology of five stages with N1 = 8, N2
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`= p* N1 = 24 where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast
`
`connections, in accordance with the invention.
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`FIG. 3E1 is a diagram 300E1 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d,s) (having a connection topology called flip network and also known as
`
`inverse shuffle exchange network) of five stages with N1 = 8, N2 = p* N1 = 24 where p =
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`3, d = 2 and s = 1, rearrangeably nonblocking network for unicast connections.
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`FIG. 3F1 is a diagram 300F1 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,d , 5) having Baseline connection topology of five stages with N1 = 8, N2 = p*
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`N1 = 24 where p = 3, d = ’7 and s = 1, rearrangeably nonblocking network for unicast
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`connections.
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`FIG. 3G1 is a diagram 300G1 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d,s) having an exemplary connection topology of five stages with N1 = 8, N2
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`= p* N1 = 24 where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast
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`connections, in accordance with the invention.
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`FIG. 3H1 is a diagram 300H1 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,d ,5) having an exemplary connection topology of five stages with N1 = 8, N2
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`= p* N1 = 24 where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast
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`connections, in accordance with the invention.
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`FIG. 311 is a diagram 30011 of an exemplary asymmetrical multi-stage network
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`V(N1, N2 , d , 5) (having a connection topology built using back-to-back Banyan Networks
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`or back-to-back Delta Networks or equivalently back-to-back Butterfly networks) of five
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`stages with N1 = 8, N2 = p* N1 = 24 where p = 3, d = 2 and s = l, rearrangeably
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`nonblocking network for unicast connections.
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`FIG. 3] 1 is a diagram 300] 1 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d,s) having an exemplary connection topology of five stages with N1 = 8, N2
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`= p* N1 = 24 where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast
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`connections.
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`FIG. 3K1 is a diagram 300K1 of a general asymmetrical multi-stage network
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`V(N1,N2,d,s) with (2xlogd N)—1 stages with N1 = p* N2 and s = 1, rearrangeably
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`nonblocking network for unicast connections in accordance with the invention.
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`FIG. 3B2 is a diagram 300B2 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d,s)
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`(having a connection topology built using back-to-back Omega
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`Networks) of five stages with N2 = 8, N1 = p* N2: ’74, where p = 3, d = 2 and s = 1,
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`rearrangeably nonblocking network for unicast connections.
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`FIG. 3A2 is a diagram 300A2 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,d , 5) having inverse Benes connection topology of five stages with N2 = 8, N1
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`= p* N2 = 24, where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for
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`unicast connections, in accordance with the invention.
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`FIG. 3C2 is a diagram 300C2 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,al , 5) having an exemplary connection topology of five stages with N2 = 8, N1
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`= p* N2 = 24, where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for
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`unicast connections, in accordance with the invention.
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`FIG. 3D2 is a diagram 300D2 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d ,s) having an exemplary connection topology of five stages with N2 = 8, N1
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`= p* N2 = 24, where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for
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`unicast connections, in accordance with the invention.
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`FIG. 3E2 is a diagram 300E2 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d,s) (having a connection topology called flip network and also known as
`
`inverse shuffle exchange network) of five stages with N2 = 8, N1 = p* N2 = 24, where p
`
`= 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast connections.
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`FIG. 3F2 is a diagram 300F2 of an exemplary asymmetrical multi-stage network
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`V(Nl, N2,61, 5) having Baseline connection topology of five stages with N2 = 8, N1 = p*
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`N2 = 24, where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for unicast
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`connections.
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`FIG. 3G2 is a diagram 300G2 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,d, 5) having an exemplary connection topology of five stages with N2 = 8, N1
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`= p* N2 = 24, where p = 3, d = ’7 and s = 1, rearrangeably nonblocking network for
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`unicast connections, in accordance with the invention.
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`FIG. 3H2 is a diagram 300H2 of an exemplary asymmetrical multi-stage network
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`V(N1,N2,d ,5) having an exemplary connection topology of five stages with N2 = 8, N1
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`= p* N2 = 24, where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for
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`unicast connections, in accordance with the invention.
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`FIG. 312 is a diagram 30012 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,d , 5) (having a connection topology built using back-to-back Banyan Networks
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`or back-to-back Delta Networks or equivalently back-to-back Butterfly networks) of five
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`stages with N2 = 8, N1 = p* N2 = 24, where p = 3, d = 2 and s = 1, rearrangeably
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`25
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`nonblocking network for unicast connections.
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`FIG. 312 is a diagram 30012 of an exemplary asymmetrical multi-stage network
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`V(N1, N2,d , 5) having an exemplary connection topology of five stages with N2 = 8, N1
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`= p* N; = 24, where p = 3, d = 2 and s = 1, rearrangeably nonblocking network for
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`unicast connections.
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`FIG. 3K2 is a diagram 300K2 of a general asymmetrical multi-stage network
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`V(N1,N2,d,s) with (leogd N)—1 stages with N2 = p* N1 and s = 1, rearrangeably
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`nonblocking network for unicast connections in accordance with the invention.
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`FIG. 4A is high-level
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`flowchart of a scheduling method according to the
`
`invention, used to set up the multicast connections in all the networks disclosed in this
`
`invention.
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`DETAILED DESCRIPTION OF THE INVENTION
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`The present invention is concerned with the design and operation of large scale
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`crosspoint reduction using arbitrarily large folded multi-stage switching networks for
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`broadcast, unicast and multicast connections. Particularly folded multi-stage networks
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`with stages more than three and radices greater than or equal to two offer large scale
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`crosspoint reduction when configured with optimal links as disclosed in this invention.
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`When a transmitting device simultaneously sends information to more than one
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`receiving device, the one-to-many connection required between the transmitting device
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`and the receiving devices is called a multicast connection. A set of multicast connections
`
`is referred to as a multicast assignment. When a transmitting device sends information to
`
`one receiving device, the one-to-one connection required between the transmitting device
`
`and the receiving device is called unicast connection. When a transmitting device
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`simultaneously sends information to all the available receiving devices, the one-to-all
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`connection required between the transmitting device and the receiving devices is called a
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`broadcast connection.
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`In general, a multicast connection is meant to be one-to-many connection, which
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`includes unicast and broadcast connections. A multicast assignment in a switching
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`network is nonblocking if any of the available inlet links can always be connected to any
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`of the available outlet links.
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`In certain folded multi-stage networks of the type described herein, any
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`connection request of arbitrary fan-out, i.e. from an inlet link to an outlet link or to a set
`
`of outlet links of the network, can be satisfied without blocking if necessary by
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`rearranging some of the previous connection requests. In certain other folded multi-stage
`
`networks of the type described herein, any connection request of arbitrary fan-out, i.e.
`
`from an inlet link to an outlet link or to a set of outlet links of the network, can be
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`satisfied without blocking with never needing to rearrange any of the previous connection
`
`requests.
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`In certain folded multi—stage networks of the type described herein, any
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`connection request of unicast from an inlet link to an outlet link of the network, can be
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`satisfied without blocking if necessary by rearranging some of the previous connection
`
`requests. In certain other folded multi-stage networks of the type described herein, any
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`connection request of unicast from an inlet link to an outlet link of the network, can be
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`satisfied without blocking with never needing to rearrange any of the previous connection
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`requests.
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`The folded multi-stage network Vfold (N1, N2, d, s) disclosed, in the current
`
`invention, is topologically exactly the same as the multi-stage network V(N1, N2 , d, s) ,
`
`disclosed in US. Provisional Patent Application Docket No. M-0037US that is
`
`incorporated by reference above, excepting that in the illustrations folded network
`
`Vfold (N1,N2 , cl, 5) is shown as it is folded at middle stage 130 +10 * (Long2 — 2) . This
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`is true for all the embodiments presented in the current invention.
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`Nonblocking configurations for other types of networks with numerous
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`connection topologies and scheduling methods are disclosed as follows:
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`1) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
`
`unicast for generalized multi-stage networks V(N1 , N2, d , s) with numerous connection
`
`topologies and the scheduling methods are described in detail in US. Provisional Patent
`
`Application, Attorney Docket No. M-0037 US that is incorporated by reference above.
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`2) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
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`unicast for generalized butterfly fat tree networks Vbfl (N1 , N2, d , s) with numerous
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`connection topologies and the scheduling methods are described in detail in US
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`Provisional Patent Application, Attorney Docket No. M-0038 US that is incorporated by
`
`reference above.
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`3) Rearrangeably nonblocking for arbitrary fan-out multicast and unicast, and
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`strictly nonblocking for unicast for generalized multi-link multi-stage networks
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`thnk (N1 ,N2 , d , s) and generalized folded multi—link multi—stage networks
`
`Vfoldwlmk (N1 , N2 , d , s) with numerous connection topologies and the scheduling methods
`
`are described in detail in US Provisional Patent Application, Attorney Docket No. M-
`
`0039 US that is incorporated by reference above.
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`4) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
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`unicast for generalized multi-link butterfly fat tree networks thnk_bfi (Nl , N2 , d , s) with
`
`numerous connection topologies and the scheduling methods are described in detail in
`
`US. Provisional Patent Application, Attorney Docket No. M-0040 US that is
`
`incorporated by reference above.
`
`5) Strictly nonblocking for arbitrary fan-out multicast for generalized multi-link
`
`multi—stage networks leink (N1, N2 , d , s) and generalized folded multi—link multi—stage
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`networks V1.0,dwhnk (N1 , N2 , d , s) with numerous connection topologies and the scheduling
`
`methods are described in detail in US. Provisional Patent Application, Attorney Docket
`
`No. M—0042 US that is incorporated by reference above.
`
`6) VLSI layouts of generalized multi-stage networks V(N1,N2,d, s) , generalized
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`folded multi-stage networks anm (N1 ,N2 , d, s), generalized butterfly fat tree networks
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`Vbfi (N1, N2 , d , s) , generalized multi-link multi-stage networks leink (N1 , N2 , d , s) ,
`
`generalized folded multi-link multi-stage networks Vfoldflnhnk (N1 , N2 , d , s) , generalized
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`multi-link butterfly fat tree networks Vm,inkibfi (N1 , N2 , d, s) , and generalized hypercube
`
`networks thbe (N1, N2,d ,5) for s = 1,2,3 or any number in general, are described in
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`-12-
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`M—0041 US
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`detail in US Provisional Patent Application, Attorney Docket No. M-0045 US that is
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`incorporated by reference above.
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`Symmetric folded RNB Embodiments:
`
`Referring to FIG. 1A, in one embodiment, an exemplary symmetrical folded
`
`multi-stage network 100A with five stages of thirty two switches for satisfying
`
`communication requests, such as setting up a telephone call or a data call, or a connection
`
`between configurable logic blocks, between an input stage 110 and output stage 120 via
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`middle stages 130, 140, and 150 is shown where input stage 110 consists of four, two by
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`four switches 131-134 and output stage 120 consists of four, four by two switches 081-
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`034. And all the middle stages namely middle stage 130 consists of eight, two by two
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`switches MS(1,1) - MS(1,8), middle stage 140 consists of eight, two by two switches
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`MS(2,1) - MS(2,8), and middle stage 150 consists of eight, two by two switches MS(3,l)
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`- MS(3,8).
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`Such a network can be operated in strictly non-blocking manner for unicast
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`connections, because the switches in the input stage 110 are of size two by four, the
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`switches in output stage 120 are of size four by two, and there are eight switches in each
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`of middle stage 130, middle stage 140 and middle stage 150. Such a network can be
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`operated in rearrangeably non-blocking manner for multicast connections, because the
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`switches in the input stage 110 are of size two by four, the switches in output stage 120
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`are of size four by two, and there are eight switches in each of middle stage 130, middle
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`stage 140 and middle stage 150.
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`In one embodiment of this network each of the input switches ISl-IS4 and output
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`switches OSl-OS4 are crossbar switches. The number of switches of input stage 110 and
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`25
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`of output stage 120 can be denoted in general with the variable E , where N is the total
`d
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`number of inlet links or outlet links. The number of middle switches in each middle stage
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`is denoted by 2X%. The size of each input switch ISl-IS4 can be denoted in general
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`M—0041 US
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`with the notation d * 2d and each output switch OSl-OS4 can be denoted in general with
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`the notation 2d >|< d . Likewise, the size of each switch in any of the middle stages can be
`
`denoted as d * d . A switch as used herein can be either a crossbar switch, or a network
`
`of switches each of which in turn may be a crossbar switch or a network of switches. A
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`symmetric folded multi-stage network can be represented with the notation Vfold (N, d, s),
`
`where N represents the total number of inlet links of all input switches (for example the
`
`links IL1-IL8), d represents the inlet links of each input switch or outlet links of each
`
`output switch, and s is the ratio of number of outgoing links from each input switch to
`
`the inlet links of each input switch. Although it is not necessary that there be the same
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`10
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`number of inlet links IL1-IL8 as there are outlet links OLl-OLS, in a symmetrical
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`network they are the same.
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`Each of the 3 input switches ISl — 134 are connected to exactly 2Xd switches
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`in middle stage 130 through 2x d links (for example input switch 131 is connected to
`
`middle switches MS(1,1), MS(1,2), MS(1,5) and MS(1,6) through the links ML(1,1),
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`15
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`ML(1,2), ML(1,3) and ML(1,4) respectively).
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`Each of the 2X% middle switches MS(1,1) — MS(1,8) in the middle stage 130
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`are connected from exactly (1 input switches through (1 links (for example the links
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`ML(1,1) and ML(1,5) are connected to the middle switch MS(1,1) from input switch 131
`
`and 132 respectively) and also are connected to exactly d switches in middle stage 140
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`through d links (for example the links ML(2,1) and ML(2,2) are connected from middle
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`switch MS(1, 1) to middle switch MS(2,1) and MS(2,3) respectively).
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`Similarly each of the 2 X% middle switches MS(2,1) — MS(2,8) in the middle
`
`stage 140 are connected from exactly d switches in middle stage 130 through d links
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`(for example the links ML(2,1) and ML(2,6) are connected to the middle switch MS(2,1)
`
`from middle switches MS(1,1) and MS(1,3) respectively) and also are connected to
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`exactly d switches in middle stage 150 through d links (for example the links ML(3,1)
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`and ML(3,2) are connected from middle switch MS(2,1) to middle switch MS(3,1) and
`
`MS(3,3) respectively).
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`Similarly each of the 2X% middle switches MS(3,1) — MS(3,8) in the middle
`
`stage 150 are connected from exactly d switches in middle stage 140 through d links
`
`(for example the links ML(3,1) and ML(3,6) are connected to the middle switch MS(3,1)
`
`from middle switches MS(2,1) and MS(2,3) respectively) and also are connected to
`
`exactly (1 output switches in output stage 120 through (1 links (for example the links
`
`ML(4,1) and ML(4,2) are connected to output switches 031 and 032 respectively from
`
`middle switches MS(3, 1)).
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`Each of the % output switches OS] — 034 are connected from exactly 2X d
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`switches in middle stage 150 through 2 X (1 links (for example output switch 081 is
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`connected from middle switches MS(3,1), MS(3,2), MS(3,5) and MS(3,6) through the
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`links ML(4,1), ML(4,3), ML(4,9) and ML(4,11) respectively).
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`Finally the connection topology of the network 100A shown in FIG. 1A is known
`
`to be back to back inverse Benes connection topology.
`
`Referring to FIG. 1A1, in another embodiment of network Vfold (N, d, s), an
`
`exemplary symmetrical folded multi-stage network 100A] with five stages of thirty two
`
`switches for satisfying communication requests, such as setting up a telephone call or a
`
`data call, or a connection between configurable logic blocks, between an input stage 110
`
`and output stage 120 via middle stages 130, 140, and 150 is shown where input stage 110
`
`consists of four, two by four switches 181-134 and output stage 120 consists of four, four
`
`by two switches OSl-OS4. And all the middle stages namely middle stage 130 consists of
`
`eight, two by two switches MS(1,1) - MS(1,8), middle stage 140 consists of eight, two by
`
`two switches MS(2,1) - MS(2,8), and middle stage 150 consists of eight, two by two
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`25
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`switches MS(3,1) - MS(3,8).
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`Such a network can be operated in strictly non-blocking manner for unicast
`
`connections, because the switches in the input stage 110 are of size two by four, the
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`M—0041 US
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`switches in output stage 120 are of size four by two, and there are eight switches in each
`
`of middle stage 130, middle stage 140 and middle stage 150. Such a network can be
`
`operated in rearrangeably non-blocking manner for multicast connections, because the
`
`switches in the input stage 110 are of size two by four, the switches in output stage 120
`
`are of size four by two, and there are eight switches in each of middle stage 130, middle
`
`stage 140 and middle stage 150.
`
`In one embodiment of this network each of the input switches 131-184 and output
`
`switches OSl-OS4 are crossbar switches. The number of switches of input stage 110 and
`
`of output stage 120 can be denoted in general with the variable E , where N is the total
`
`number of inlet links or outlet links. The number of middle switches in each middle stage
`
`is denoted by Zxfl. The size of each input switch ISl-IS4 can be denoted in general
`d
`
`with the notation cl * 2d and each output switch OSl-OS4 can be denoted in general with
`
`the notation 2d * d . Likewise, the size of each switch in any of the middle stages can be
`
`denoted as d * d . A switch as used herein can be either a crossbar switch, or a network
`
`of switches each of which in turn may be a crossbar switch or a network of switches. The
`
`symmetric folded multi-stage network of FIG. 1A1 is also the network of the type
`
`VJW (N, d, s), where N represents the total number of inlet links of all input switches
`
`(for example the links ILl-ILS), d represents the inlet links of each input switch or outlet
`
`links of each output switch, and s is the ratio of number of outgoing links from each
`
`input switch to the inlet links of each input switch. Although it is not necessary that there
`
`be the same number of inlet links ILl-ILS as there are outl