M-0039 US
`
`FULLY CONNECTED GENERALIZED REARRANGEABLY NONBLOCKING
`
`MULTI-LINK MULTI-STAGE NETWORKS
`
`Venkat Konda
`
`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-0037USentitled "FULLY CONNECTED
`
`GENERALIZED MULTI-STAGE NETWORKS"by Venkat Kondaassigned to the same
`
`10
`
`assignee as the current application,filed concurrently.
`
`This application is related to and incorporates by referencein its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0038USentitled "FULLY CONNECTED
`
`GENERALIZED BUTTERFLY FAT TREE NETWORKS"by Venkat Konda assigned
`
`to the same assignee as the current application, filed concurrently.
`
`15
`
`This application is related to and incorporates by referencein its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0040USentitled "FULLY CONNECTED
`
`GENERALIZED MULTI-LINK BUTTERFLY FAT TREE NETWORKS" by Venkat
`
`Konda assigned to the sameassignee as the current application, filed concurrently.
`
`This application is related to and incorporates by referencein its entirety the U.S.
`
`20
`
`Provisional Patent Application Docket No. M-0041USentitled "FULLY CONNECTED
`
`GENERALIZED FOLDED MULTI-STAGE NETWORKS"by Venkat Kondaassigned
`
`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-0042USentitled "FULLY CONNECTED
`
`GENERALIZED STRICTLY NONBLOCKING MULTI-LINK MULTISTAGE
`
`NETWORKS"by Venkat Konda assigned to the same assignee as the current application,
`
`filed concurrently.
`
`-|-
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`Page 1 of 140
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`FLEX LOGIX EXHIBIT 1021
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`FLEX LOGIX EXHIBIT 1021
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`M-0039 US
`
`This application is related to and incorporates by referencein its entirety the U.S.
`
`Provisional Patent Application Docket No. M-0045USentitled "VLSI LAYOUTS OF
`
`FULLY CONNECTED GENERALIZED NETWORKS"by Venkat Kondaassigned to
`
`the same assignee as the current application, filed concurrently.
`
`BRIEF DESCRIPTION OF DRAWINGS
`
`FIG. 1A is a diagram 100A of an exemplary symmetrical multi-link multi-stage
`
`network V,,,,,,(N,d,s5) having inverse Benes connection topologyof five stages with N =
`
`8, d = 2 and s=2,strictly nonblocking network for unicast connections and rearrangeably
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`10
`
`invention.
`
`FIG. 1B is a diagram 100B of an exemplary symmetrical multi-link multi-stage
`
`network V_,,,.(N,d,s)
`
`(having a connection topology built using back-to-back Omega
`
`Networks) of five stages with N = 8, d = 2 and s=2, strictly nonblocking network for
`
`unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`15
`
`multicast connections, in accordance with the invention.
`
`FIG. 1C is a diagram 100C of an exemplary symmetrical multi-link multi-stage
`
`network V_,,,,(NV.d,s) having an exemplary connection topology of five stages with N =
`
`8, d = 2 and s=2, strictly nonblocking network for unicast connections and rearrangeably
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`20
`
`invention.
`
`FIG. 1D is a diagram 100D of an exemplary symmetrical multi-link multi-stage
`
`network V“inn (N.d,S) having an exemplary connection topology of five stages with N =
`
`8, d = 2 and s=2, strictly nonblocking network for unicast connections and rearrangeably
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`25
`
`invention.
`
`FIG. 1E is a diagram 100E of an exemplary symmetrical multi-link multi-stage
`
`network Vmiink (N,d,s) (having a connection topology called flip network and also known
`
`as inverse shuffle exchange network) of five stages with N = 8, d = 2 and s=2,strictly
`-2-
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`M-0039 US
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`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG, 1F is a diagram 100F of an exemplary symmetrical multi-link multi-stage
`
`network Vming (N.@,5) having Baseline connection topology of five stages with N = 8, d
`
`= 2 and s=2, strictly nonblocking network for unicast connections and rearrangeably
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`FIG. 1G is a diagram 100G of an exemplary symmetrical multi-link multi-stage
`
`network V,,,,,(N.d,s) having an exemplary connection topologyoffive stages with N =
`
`10
`
`8, d = 2 and s=2,strictly nonblocking network for unicast connections and rearrangeably
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`FIG. 1H is a diagram 100H of an exemplary symmetrical multi-link multi-stage
`
`network V,_,,,,(N.d,s) having an exemplary connection topologyoffive stages with N =
`
`15
`
`8, d = 2 and s=2,strictly nonblocking network for unicast connections and rearrangeably
`
`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`FIG, 11 is a diagram 1001 of an exemplary symmetrical multi-link multi-stage
`
`network V,,,,,(V.d,s) (having a connection topology built using back-to-back Banyan
`
`20
`
`Networks or back-to-back Delta Networks or equivalently back-to-back Butterfly
`
`networks) of five stages with N = 8, d = 2 and s=2, strictly nonblocking network for
`
`unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`FIG. 1J is a diagram 100J of an exemplary symmetrical multi-link multi-stage
`
`25
`
`network V,,,,,(N.d,s) having an exemplary connection topologyoffive stages with N =
`
`8, d = 2 and s=2,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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`M-0039 US
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`FIG, 1K is a diagram 100K of a general symmetrical multi-link multi-stage
`network V,,,,,(N,d,s) with (2xlog,N)—1 stages with s=2,
`strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking network for arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`FIG. 1A1 is a diagram 100A1 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,(N,,N,,d,s) having inverse Benes connection topology of five
`
`stages with N; = 8, No = p* N; = 24 where p = 3, d = 2 and s = 2, strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking networkfor arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`10
`
`FIG. 1B1 is a diagram 100B1 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,,,(N,,N>,d,5) (having a connection topology built using back-to-back
`
`Omega Networks) of five stages with N; = 8, No = p* N; = 24 where p= 3, d=2 ands =
`
`2, strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`networkfor arbitrary fan-out multicast connections, in accordance with the invention.
`
`15
`
`FIG. 1C1 is a diagram 100C1 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,,(N,,N,,d,s) having an exemplary connection topology of five
`
`stages with N; = 8, No = p* Ni = 24 where p = 3, d = 2 and s = 2, strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking networkfor arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`20
`
`FIG. 1D1 is a diagram 100D1 of an exemplary asymmetrical multi-link multi-
`
`stage network V__,,(N,,N,,d,s) having an exemplary connection topology of five stages
`
`with N; = 8, No = p* N; = 24 where p = 3, d = 2 and s = 2,strictly nonblocking network
`
`for unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`25
`
`FIG. 1E1 is a diagram 100E1 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,.(N,,N,,d,5) (having a connection topology called flip network and
`
`also knownas inverse shuffle exchange network) of five stages with N; = 8, No = p* Ni
`
`= 24 where p = 3, d = 2 and s = 2,strictly nonblocking network for unicast connections
`
`4.
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`M-0039 US
`
`and rearrangeably nonblocking network for arbitrary fan-out multicast connections, in
`
`accordance with the invention.
`
`FIG, 1F1 is a diagram 100F1 of an exemplary asymmetrical multi-link multi-stage
`
`network V,_,,,,(NV,,N,,d,s5) having Baseline connection topology of five stages with N; =
`
`8, No =p* N; = 24 where p = 3, d= 2 and s = 2,strictly nonblocking network for unicast
`
`connections and rearrangeably nonblocking network for arbitrary fan-out multicast
`
`connections, in accordance with the invention.
`
`FIG. 1G1 is a diagram 100G1 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,(N,,N,,d,s) having an exemplary connection topology of five
`
`10
`
`stages with N; = 8, N2 = p* N; = 24 where p = 3, d = 2 and s = 2,strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking network for arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`FIG. 1H1 is a diagram 100H1 of an exemplary asymmetrical multi-link multi-
`
`stage network V,“ning (N»N>,d,5) having an exemplary connection topology of five
`
`15
`
`stages with N; = 8, No = p* N; = 24 where p = 3, d = 2 and s = 2,strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking network for arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`FIG, 111 is a diagram 10011 of an exemplary asymmetrical multi-link multi-stage
`
`network V,,,,(N,,N,.d.s)
`
`(having a connection topology built using back-to-back
`
`20
`
`Banyan Networks or back-to-back Delta Networks or equivalently back-to-back Butterfly
`
`networks) of five stages with N; = 8, No = p* Ni = 24 where p = 3, d = 2 ands = 2,
`
`strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`networkfor arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG, 1J1 is a diagram 100J1 of an exemplary asymmetrical multi-link multi-stage
`
`25
`
`network V,,,,(N,.N,.d,s) having an exemplary connection topology of five stages with
`
`N, =8, No =p* N; = 24 where p = 3, d= 2 and s = 2, strictly nonblocking network for
`
`unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`-5-
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`M-0039 US
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`FIG, 1K1 is a diagram 100K1 of a general asymmetrical multi-link multi-stage
`network V_,,,,(N,,N,,d,s) with (2xlog, N)-1 stages with N; = p* N> and s = 2,
`
`strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`networkfor arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 1A2 is a diagram 100A2 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,(N,,N,,d,s) having inverse Benes connection topology of five
`
`stages with N. = 8, N; = p* No = 24, where p = 3, d = 2 and s = 2,strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking networkfor arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`10
`
`FIG. 1B2 is a diagram 100B2 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,,,(N,,N>,d,5) (having a connection topology built using back-to-back
`
`Omega Networks) of five stages with Nz = 8, N; = p* No= 24, where p=3,d=2 ands
`
`= 2, strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`networkfor arbitrary fan-out multicast connections, in accordance with the invention.
`
`15
`
`FIG. 1C2 is a diagram 100C2 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,,(N,,N,,d,s) having an exemplary connection topology of five
`
`stages with No = 8, Ni = p* No= 24, where p = 3, d = 2 and s = 2,strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking networkfor arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`20
`
`FIG. 1D2 is a diagram 100D2 of an exemplary asymmetrical multi-link multi-
`
`stage network V__,,(N,,N,,d,s) having an exemplary connection topology of five stages
`
`with N» = 8, N; = p* No= 24, where p = 3, d=2and s = 2,strictly nonblocking network
`
`for unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`25
`
`FIG. 1E2 is a diagram 100E2 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,.(N,,N,,d,5) (having a connection topology called flip network and
`
`also knownas inverse shuffle exchange network) of five stages with No = 8, N; = p* No
`
`= 24, where p = 3, d= 2 and s = 2,strictly nonblocking network for unicast connections
`
`-6-
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`M-0039 US
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`and rearrangeably nonblocking network for arbitrary fan-out multicast connections, in
`
`accordance with the invention.
`
`FIG, 1F2 is a diagram 100F2 of an exemplary asymmetrical multi-link multi-stage
`
`network V,_,,,,(V,,N,,d,s5) having Baseline connection topology of five stages with N2 =
`
`8, Ni = p* No = 24, where p = 3, d = 2 and s = 2,strictly nonblocking network for
`
`unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`FIG, 1G2 is a diagram 100G2 of an exemplary asymmetrical multi-link multi-
`
`stage network V,,,,(N,,N,,d,s) having an exemplary connection topology of five
`
`10
`stages with No = 8, N; = p* N,=24, where p = 3, d =2and s = 2,strictly nonblocking
`
`network for unicast connections and rearrangeably nonblocking network for arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`FIG, 1H2 is a diagram 100H2 of an exemplary asymmetrical multi-link multi-
`
`stage network V,“ning (N,N>,d,5) having an exemplary connection topology offive stages
`
`15
`with No = 8, N; = p* No= 24, where p = 3, d=2ands = 2,strictly nonblocking network
`
`for unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`FIG, 112 is a diagram 10012 of an exemplary asymmetrical multi-link multi-stage
`
`network V,,,,(N,,N,.d.s)
`
`(having a connection topology built using back-to-back
`
`20
`
`Banyan Networks or back-to-back Delta Networks or equivalently back-to-back Butterfly
`
`networks) of five stages with No = 8, N; = p* N2= 24, where p = 3, d =2 ands =2,
`
`strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`networkfor arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG, 1J2 is a diagram 100J2 of an exemplary asymmetrical multi-link multi-stage
`
`25
`
`network V,,,,(N,.N,.d,s) having an exemplary connection topology of five stages with
`
`Nz =8, N; = p* No= 24, where p = 3, d = 2 and s = 2,strictly nonblocking network for
`
`unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections, in accordance with the invention.
`
`-7-
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`FIG, 1K2 is a diagram 100K2 of a general asymmetrical multi-link multi-stage
`network V_,,,,(N,,N,,d,s) with (2xlog, N)-1 stages with N. = p* N, and s = 2,
`
`strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`networkfor arbitrary fan-out multicast connections, in accordance with the invention.
`
`FIG. 2A is a diagram 200A of an exemplary symmetrical folded multi-link multi-
`
`stage network Vi141sning (N.d, 5) having inverse Benes 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 networkfor arbitrary fan-
`
`out multicast connections, in accordance with the invention.
`
`10
`
`FIG. 2B is a diagram 200B of a general symmetrical folded multi-link multi-stage
`network Vigoniine(N>d,2) with (2xlog, N)—-1 stagesstrictly nonblocking network for
`
`unicast connections and rearrangeably nonblocking network for arbitrary fan-out
`
`multicast connections in accordance with the invention.
`
`FIG, 2C is a diagram 200C of an exemplary asymmetrical folded multi-link multi-
`
`15
`
`stage network Voitmine (N,,N>,d,2) having inverse Benes connection topology of five
`
`stages with N; = 8, No = p* N; = 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.
`
`20
`
`FIG, 2D is a diagram 200D of a general asymmetrical folded multi-link multi-
`va-mtingN,»N,,d,2) with No = p* N; and with (2xlog, N)—-1 stages
`
`‘0.
`stage network V,
`
`strictly nonblocking network for unicast connections and rearrangeably nonblocking
`
`network for arbitrary fan-out multicast connections in accordance with the invention.
`
`FIG, 2E is a diagram 200E of an exemplary asymmetrical folded multi-link multi-
`
`25
`
`stage network Viiimine(N,,N.,d,2) having inverse Benes connection topology of five
`
`stages with No = 8, N; = p* No = 24, where p = 3, and d = 2 with exemplary multicast
`
`connections, strictly nonblocking network for unicast connections and rearrangeably
`
`-8-
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`M-0039 US
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`nonblocking network for arbitrary fan-out multicast connections, in accordance with the
`
`invention.
`
`FIG, 2F is a diagram 200F of a general asymmetrical folded multi-link multi-stage
`network Vigig mine(Ni.N>,d,2) with Ni = p* No and with (2xlog, N)-1 stagesstrictly
`
`nonblocking network for unicast connections and rearrangeably nonblocking network for
`
`arbitrary fan-out multicast connections in accordance with the invention.
`
`FIG. 3A is high-level flowchart of a scheduling method according to the
`
`invention, used to set up the multicast connections in all the networks disclosed in this
`
`invention.
`
`10
`
`DETAILED DESCRIPTION OF THE INVENTION
`
`The present invention is concerned with the design and operation of large scale
`
`crosspoint reduction using arbitrarily large multi-link multi-stage switching networks for
`
`broadcast, unicast and multicast connections, Particularly multi-link multi-stage networks
`
`15
`
`with stages more than three and radices greater than or equal to two offer large scale
`
`crosspoint reduction when configured with optimallinks as disclosed in this invention.
`
`Whena transmitting device simultaneously sends information to more than one
`
`receiving device, the one-to-many connection required between the transmitting device
`
`and the receiving devices is called a multicast connection. A set of multicast connections
`
`20
`
`is referred to as a multicast assignment. Whena 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
`
`simultaneously sends information to all the available receiving devices, the one-to-all
`
`connection required betweenthe transmitting device and the receiving devicesis called a
`
`25
`
`broadcast connection.
`
`In general, a multicast connection is meant to be one-to-many connection, which
`
`includes unicast and broadcast connections. A multicast assignmentin a switching
`
`-9-
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`M-0039 US
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`network is nonblocking if any of the available inlet links can always be connected to any
`
`of the available outlet links.
`
`In certain multi-link 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 satisfied without blocking if necessary by
`
`rearranging someof the previous connection requests. In certain other multi-link 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
`
`satisfied without blocking with never needing to rearrange any of the previous connection
`
`10
`
`requests,
`
`In certain multi-link multi-stage networks of the type described herein, any
`
`connection request of unicast from aninlet link to an outlet link of the network, can be
`
`satisfied without blocking if necessary by rearranging some of the previous connection
`
`requests. In certain other multi-link multi-stage networks of the type described herein,
`
`15
`
`any connection request of unicast from an inlet link to an outlet link of the network, can
`
`be satisfied without blocking with never needing to rearrange any of the previous
`
`connection requests.
`
`Nonblocking configurations for other types of networks with numerous
`
`connection topologies and scheduling methodsare disclosed as follows:
`
`20
`
`1) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
`
`unicast for generalized multi-stage networks V(N,,N,,d,s) with numerous connection
`
`topologies and the scheduling methods are described in detail in U.S. Provisional Patent
`
`Application, Attorney Docket No. M-0037 USthat is incorporated by reference above.
`
`2) Strictly and rearrangeably nonblockingfor arbitrary fan-out multicast and
`
`25
`
`unicast for generalized butterfly fat tree networks V,,(N,,N,,d,s) with numerous
`
`connection topologies and the scheduling methods are described in detail] in U.S.
`
`Provisional Patent Application, Attorney Docket No. M-0038 USthat is incorporated by
`
`reference above.
`
`-10-
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`3) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
`
`unicast for generalized multi-link butterflyfat tree networks V,jin,_y¢(N,,N2,d,s) with
`
`numerous connection topologies and the scheduling methods are described in detail in
`
`U.S. Provisional Patent Application, Attorney Docket No. M-0040 USthatis
`
`incorporated by reference above.
`
`4) Strictly and rearrangeably nonblocking for arbitrary fan-out multicast and
`
`unicast for generalized folded multi-stage networks V,,.,(N,,N,,d,5) with numerous
`
`connection topologies and the scheduling methodsare described in detail in U.S.
`
`Provisional Patent Application, Attorney Docket No. M-0041 USthat is incorporated by
`
`10
`
`reference above.
`
`5) Strictly nonblocking for arbitrary fan-out multicast for generalized multi-link
`
`multi-stage networks V,,,,,,(N,,N,,.d,s) and generalized folded multi-link multi-stage
`
`networks Vii4-miine(N,N,,d, 5) with numerous connection topologies and the scheduling
`
`methods are described in detail in U.S. Provisional Patent Application, Attorney Docket
`
`15
`
`No. M-0042 USthat is incorporated by reference above.
`
`6) VLSI layouts of generalized multi-stage networks V(N,,N,,d,5), generalized
`
`folded multi-stage networks V,,,(N,,N,.d,s5), generalized butterfly fat tree networks
`
`Vi,(N,,N,,d,5), generalized multi-link multi-stage networks V,,,,(N,,N,,d,5),
`
`generalized folded multi-link multi-stage networks V,0.ia_mine (N1,N>,d,8), generalized
`
`20
`
`multi-link butterfly fat tree networks V,mnlink-of (N,N,,d, 5), and generalized hypercube
`
`networksV,_,,,(V,,N.,,d,s) for s = 1,2,3 or any numberin general, are described in
`
`detail in U.S. Provisional Patent Application, Attorney Docket No. M-0045 USthatis
`
`incorporated by reference above.
`
`Symmetric RNB Embodiments:
`
`Referring to FIG. 1A, in one embodiment, an exemplary symmetrical multi-link
`
`multi-stage network 100A with five stages of twenty switches for satisfying
`
`communication requests, such as setting up a telephone call or a data call, or a connection
`
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`between configurable logic blocks, between an input stage 110 and outputstage 120 via
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`middle stages 130, 140, and 150 is shown whereinput stage 110 consists of four, two by
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`four switches IS1-IS4 and output stage 120 consists of four, four by two switches OS1-
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`OS4. And all the middle stages namely middle stage 130 consists of four, four by four
`
`switches MS(1,1) - MS(1,4), middle stage 140 consists of four, four by four switches
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`MS(2,1) - MS(2,4), and middle stage 150 consists of four, four by four switches MS(3,1)
`
`- MS(3,4).
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`Such a network can be operated in strictly non-blocking mannerfor unicast
`
`connections, because the switches in the input stage 110 are of size two by four, the
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`10
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`switches in output stage 120 are of size four by two, and there are four 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 four switches in each of middle stage 130, middle
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`15
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`stage 140 and middle stage 150.
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`In one embodimentof this network each of the input switches I$ 1-I$4 and output
`
`switches O$1-OS4are crossbar switches. The number of switches of input stage 110 and
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`ofoutput stage 120 can be denoted in general with the variable - , where N is the total
`
`numberofinlet links or outlet links. The number of middle switches in each middle stage
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`20
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`is denoted by = . The size of each input switch [S1-IS4 can be denoted in general with
`
`the notation d *2d and each output switch OS1-OS4can be denoted in general with the
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`notation 2d *d. Likewise, the size of each switch in any of the middle stages can be
`
`denoted as 2d *2d . A switch as used herein can be either a crossbar switch, or a
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`network of switches each of which in turn may be a crossbar switch or a network of
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`25
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`switches. A symmetric multi-link multi-stage network can be represented with the
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`notation Vmink (N,d,8), Where N represents the total numberofinletlinks ofall 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, Althoughit is not necessary that
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`there be the same numberofinlet links IL1-IL8 as there are outlet links OL1-OL8, in a
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`symmetrical network they are the same.
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`Eachof the - input switches IS1 —IS4 are connected to exactly 2xd switches
`
`in middle stage 130 through 2xd links (for example input switch IS1 is connected to
`
`middle switch MS(1,1) through the links ML(1,1), ML(1,2), and also to middle switch
`
`MS(1,2) through the links ML(1,3) and ML(1,4)).
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`Eachof the - middle switches MS(1,1) — MS(1,4) in the middle stage 130 are
`
`connected from exactly d input switches through 2xd links (for example the links
`
`ML(1,1) and ML(1,2) are connected to the middle switch MS(1,1) from input switch IS1,
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`10
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`and the links ML(1,7) and ML(1,8) are connected to the middle switch MS(1,1) from
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`input switch LS?) and also are connected to exactly d switches in middle stage 140
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`through 2xd_ links (for example the links MLQ,1) and ML(2,2) are connected from
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`middle switch MS(1,1) to middle switch MS(Q,1), and the links ML(Q,3) and ML(,4) are
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`connected from middle switch MS(1,1) to middle switch MS(2,3)).
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`15
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`Similarly each of the
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`middle switches MS(2,1) — MS(2,4) in the middle stage
`
`140 are connected from exactly d switches in middle stage 130 through 2x d links (for
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`example the links ML(2,1) and ML(2,2) are connected to the middle switch MS(,1) from
`
`middle switch MS(1,1), and the links ML(2,11) and ML(2,12) are connected to the
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`middle switch MS(2,1) from middle switch MS(1,3)) and also are connected to exactly d
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`20
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`switches in middle stage 150 through 2xd links (for example the links ML(3,1) and
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`ML(3,2) are connected from middle switch MS(2,1) to middle switch MS(3,1), and the
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`links ML(3,3) and ML(3,4) are connected from middle switch MS(2,1) to middle switch
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`MS(3,3)).
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`Similarly each of the = middle switches MS(3,1) — MS(3,4) in the middle stage
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`25
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`150 are connected from exactly d switches in middle stage 140 through 2x d links (for
`
`example the links ML(3,1) and ML(3,2) are connected to the middle switch MS(3,1) from
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`middle switch MS(2,1), and the links ML(3,11) and ML(3,12) are connected to the
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`middle switch MS(3,1) from middle switch MS(@,3)) and also are connected to exactly d
`
`output switches in output stage 120 through 2xd_ links (for example the links ML(4,1)
`
`and ML(4,2) are connected to output switch OS1 from Middle switch MS(3, 1), and the
`
`links ML(4,3) and ML(4,4) are connected to output switch OS2 from middle switch
`
`MS(3, 1)).
`
`Eachofthe = output switches OS1 — OS4 are connected from exactly 2xd
`
`switches in middle stage 150 through 2xd links (for example output switch OS1 is
`
`connected from middle switch MS(3,1) through the links ML(4,1) and ML(4,2), and
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`10
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`output switch OS1 is also connected from middle switch MS(3,2) through the links
`
`ML(4,7) and ML(4,8)).
`
`Finally the connection topology of the network 100A shownin FIG. 1A is known
`
`to be back to back inverse Benes connection topology.
`
`Referring to FIG. 1B, in another embodimentof network V,,,,,,(N,d,s) , an
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`15
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`exemplary symmetrical multi-link multi-stage network 100B with five stages of twenty
`
`switches for satisfying communication requests, such as setting up a telephonecall 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 IS1-IS4 and output stage 120 consists of four, four
`
`20
`
`by two switches OS1-OS4. And all the middle stages namely middle stage 130 consists of
`
`four, four by four switches MS(1,1) - MS(1,4), middle stage 140 consists of four, four by
`
`four switches MS(2,1) - MS(2,4), and middle stage 150 consists of four, four by four
`
`switches MS(3,1) - MS(3,4).
`
`Such a network can be operatedin strictly non-blocking mannerfor unicast
`
`25
`
`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 four switches in each
`
`of middle stage 130, middle stage 140 and middle stage 150. Such a network can be
`
`operated in rearrangeably non-blocking mannerfor multicast connections, because the
`
`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 four switches in each of middle stage 130, middle
`
`stage 140 and middle stage 150.
`
`In one embodimentof this network each of the input switches I$ 1-IS4 and output
`
`switches O$1-OS4are crossbar switches. The number of switches of input stage 110 and
`
`of output stage 120 can be denoted in general with the variable - , where N is the total
`
`numberofinlet links or outlet links. The number of middle switches in each middle stage
`
`is denoted by = . The size of each input switch [S1-IS4 can be denoted in general with
`
`the notation d*2d and each output switch OS1-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
`
`10
`
`denoted as 2d * 2d. A switch as used herein can be either a crossbar switch, or a
`
`network of switches each of which in turn maybe a crossbar switch or a network of
`
`switches. The symmetric multi-link multi-stage network of FIG. 1B is also the network of
`
`the type V,,,,.(N,d,s5), where N represents the total numberof inletlinks ofall input
`
`switches (for example the links IL1-IL8), d represents the inlet links of each input switch
`
`15
`
`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, Althoughit is not necessary that
`
`there be the same numberofinlet links IL1-IL8 as there are outlet links OL1-OL8, in a
`
`symmetrical network they are the same.
`
`Eachofthe ot input switches IS1 — IS4 are connected to exactly 2xd switches
`
`20
`
`in middle stage 130 through 2xd links (for example input switch IS1 is connected to
`
`middle switch MS(1,1) through the links ML(1,1), ML(1,2), and also to middle switch
`
`MS(1,2) through the links ML(1,3) and ML(1,4)).
`
`Each ofthe ot middle switches MS(1,1) — MS(1,4) in the middle stage 130 are
`
`connected from exactly d input switches through 2xd links (for example the links
`
`25
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`ML(1,1) and ML(1,2) are connected to the middle switch MS(1,1) from input switch IS1,
`
`and the links ML(1,9) and ML(1,10) are connected to the middle switch MS(1,1) from
`
`input switch IS3) and also are connected to exactly d switches in middle stage 140
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