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Shuffle Exchange Networks Explained
- 1. SHUFFLE EXCHANGE NETWORKS A G A L DANUSHKA - SEU/IS/14/PS/101 - PS0722
- 2. CONTENT β’ Introduction β’ Perfect Shuffle Vs Inverse Perfect Shuffle β’ Perfect Shuffle Interconnection Network β’ Perfect Shuffle Implementation β’ Examples β’ Applications β’ Problems β’ Summary 2SHUFFLE EXCHANGE NETWORKS
- 3. INTRODUCTION β’ Shuffle Exchange Network (SEN) is a unique path it has only a single path between a particular input and output. β’ These networks are frequently applied with simple modular switches, make use of two input and two output switching elements. β’ Shuffle exchange network suitable in multistage interconnection network architecture because it can provide an alternative path for routing procedure. 3SHUFFLE EXCHANGE NETWORKS
- 4. PERFECT SHUFFLE VS INVERSE PERFECT SHUFFLE perfect shuffle Inverse perfect shuffle 4SHUFFLE EXCHANGE NETWORKS
- 5. PERFECT SHUFFLE INTERCONNECTION NETWORK ο± Let N; no. of processors where; π0 , π1 , π πβ1 ο± N is power of 2 ο± There are one way link between each pair of processors ππ to ππ ; where 2π πππ 0 β€ π β€ π 2 β 1 2π + 1 β π πππ π 2 β€ π β€ π β 1 (Basic permutation for the perfect shuffle network.) j = 5SHUFFLE EXCHANGE NETWORKS
- 6. SHUFFLE-EXCHANGE NETWORK WITH N = 23 PROCESSORS 6SHUFFLE EXCHANGE NETWORKS 2π πππ 0 β€ π β€ π 2 β 1 2π + 1 β π πππ π 2 β€ π β€ π β 1 Solving the equation for N=8 j = j= 2i for 0 β€ i β€ 3 j= 2i-7 for 4 β€ i β€ 7 For i=0 to 3 ; (π0 , π1 , π2, π3 ; π β ππππππ π ππ) Links will be β’ i=0 ο 2i ο 0 β’ i=1 ο 2i ο 2 β’ i=2 ο 2i ο 4 β’ i=3 ο 2i ο 6 π0 ο π0 π1 ο π2 π2 ο π4 π3 ο π6 For i=4 to 7 ; (π4 , π5 , π6, π7 ) Links will be β’ i=4 ο 2i-7 ο 1 β’ i=5 ο 2i-7 ο 3 β’ i=6 ο 2i-7 ο 5 β’ i=7 ο 2i-7 ο 7 π4 ο π1 π5 ο π3 π6 ο π5 π7 ο π7 Therefore the range is 0 to 7
- 7. SHUFFLE-EXCHANGE NETWORK WITH N = 23 PROCESSORS CONT.. SHUFFLE EXCHANGE NETWORKS 7 Shuffle Connections Exchange Links 0 1 2 3 4 5 6 7 π0 ο π0 π1 ο π2 π2 ο π4 π3 ο π6 π4 ο π1 π5 ο π3 π6 ο π5 π7 ο π7
- 8. SHUFFLE EXCHANGE NETWORKS 8 ο§ N=2 π ο§ N = 8 ; 23 ο§ Then k=3; After 3 operations that particular value will be add its original location.β¦ 1 2 4 3 5 6 Necklace Short Necklace 0 7 NECKLACES SHUFFLE-EXCHANGE NETWORK
- 9. IMPLEMENTATION OF PERFECT SHUFFLE SHUFFLE EXCHANGE NETWORKS 9 01. Define a array of length n and initialize processor numbers 02. Shuffle First Half 03. Shuffle Second Half
- 10. SHUFFLE β EXCHANGE NETWORK EXAMPLES 1. Banyan Network There are n= log2 π stages each consisting of N/2 active πΈ1 nodes, which successive stages connected by passive π½π permutations. SHUFFLE EXCHANGE NETWORKS 10
- 11. SHUFFLE β EXCHANGE NETWORK EXAMPLES 2. The Omega Network β’ Multistage interconnection network. β’ The outputs from each stage are connected to the inputs of the next stage using a perfect shuffle connection system. SHUFFLE EXCHANGE NETWORKS 11
- 12. SHUFFLE EXCHANGE NETWORK APPLICATIONS Shuffle exchange network provides suitable interconnection patterns for implementing certain parallel algorithms such as; SHUFFLE EXCHANGE NETWORKS 12 β’ Polynomial evaluation β’ Fast Fourier Transform(FFT) β’ Sorting β’ Matrix transposition
- 13. PROBLEMS WITH SHUFFLE EXCHANGE SHUFFLE EXCHANGE NETWORKS 13 β’ A large shuffle-exchange network does not decompose well into smaller separate shuffle exchange networks. β’ In a large shuffle-exchange network, a small percentage of nodes will be hot spots β’ They will encounter much heavier traffic
- 14. SUMMARY 14SHUFFLE EXCHANGE NETWORKS Shuffle Exchange Processor nodes n=π π Switch nodes n Diameter 2log n β 1 Bisection Width ο(n/ log n) Edges/nodes 2 Constant edge length No
Editor's Notes
- *Multistage Interconnection Networks (MINs) are design to provide an effective communication in switching. *MINs networks consist of stages that can route the switching through the path. In this types of network the major problem occur when the switch failed to route in the stage. If these situations occur the switching need to be route to an alternative path to avoid from system failure. Shuffle-exchange networks have been widely considered as practical interconnection systems due to their size of it switching elements and uncomplicated configuration. It can helps in fault tolerance and reduce the latency. The shuffle exchange multistage interconnection network is one network in large class topologically equivalent MINs that include the omega, indirect binary, cube, baseline, and generalized cube
- Shuffle exchange network model is based on two routing functions, shuffle and exchange. A perfect shuffle cuts the deck into two halves from the center and then inter mixes them evenly. Inverse perfect shuffle does the opposite to restore the original ordering as shown in figure.
- Basic permutation for the perfect shuffle network.
- 0 & 7 are connected to it self and not connected to the remaining network. So 0 is considering as the EVEN NO. PROCESSOR. Then we make above dash lines as exchange links. These links should be created with even no. processors. So 7 also would be connected with the network. Exchange link (E) between node i and node i+1 when i is even ( = node numbers differ only in LSB) β’ bidirectional Shuffle link (S) to node LeftCycle(i) β’ unidirectional
- K Shuffling operations moves are datum or data values back to the original location. As for 8; k=3; that means after the 3 operations that particular value will be add its original location. Look at particular processes These particular designs are called necklace. Remaining one is 0; which have less no. of k operations.
- FFT is an algorithm that computes the DISCRETR FOURIER TRANSFORM of a sequence, or its inverse. Converts a signal from its original domain to a representation in the frequency domain and vice versa. Sorting ; Arrange a set of keys, stored one per processor, so that the ith processor holds the ith key in ascending order
- Issues that related to the network performance ; The sizes of network using in that networks. The technique use. The network , *can cause a complexity *can increase the cost *can cause a system failure ; By using a large network size A major problem in SEN is path complexity occur when the routing procedure have been apply. A critical set of components is defined as set of switching component, each from different groups, such as that a network a network failure will occur if all the components become faulty simultaneously [3]. SEN provide more redundant paths, by adding stage to the SEN. This network allows two paths for communication between each source and destination. SENs in addition designed to provide inter process communication and developed fault tolerant architecture. SENs functionality also can reduce the cost and latency in the interconnection process
- Diameter ; The largest distance between two nodes. Bisection width ; The minimum number of edges that must be removed to divide the network into to halves (within one) Number of edges per node ; we consider this to be the best if this is constant Maximum edge length ; we consider this to be the best if this is constant (independent of number of processors, because it affects the scalability.)