Concept of permutation network, Computer Networking

Concept Of Permutation Network

In permutation interconnection networks the information replace requires data transfer from input set of nodes to output set of nodes and likely connections among edges are established  by  applying  a variety of  permutations  in  available  links.  There  are  a variety of networks where multiple paths from source to destination are feasible.  For finding out what the feasible routes in such networks are the learning of the permutation theory is a must.

Let us see,  the basic concepts of permutation with respect to interconnection network. Let us say the network has place of n input nodes and n output nodes.

Permutation P for a network of 5 nodes (i.e., n = 5) is written as follows:

                                                             1110_Concept Of Permutation Network.png

It means that node connections are 1↔5, 2↔ 4, 3↔1, 4↔3,  5↔2.

The connections are shown in the Figure .

                                   2184_Concept Of Permutation Network 1.png

                                     299_Concept Of Permutation Network 2.png

In these examples, only one set of links exist among input and output nodes and means it is a one stage network.  It may be possible that there exist many  links among input and output (i.e. multistage network).  Permutation of all these in a multistage network are known permutation group and these are represented by a cycle e.g. permutation

P= (1,2,3) (4,5) means the network has two sets of input and output nodes, one set consists of nodes 1,2,3 and another group exists of nodes 4,5 and connections are 1→2, 2→3, 3→1, and 4→5. Here set (1,2,3) has period 3 and (4,5) has period 2, collectively these sets has periodicity 3×2=6.

Interconnection  from all  the  feasible  input  nodes  to  all  the  output  nodes  figured  the permutation group.

The permutations can be combined. This is called composition operation. In composition operation more than two permutations are applied in sequence, e.g. if P1 and P2 are two permutations defined as:

                                        1491_Concept Of Permutation Network 3.png

                                           1549_Concept Of Permutation Network 4.png

Composition of those permutations P1 P2 are characterized in Figures 14 (a) and 14 (b).There are some permutations of special significance in interconnection network.  These permutations are given by hardware. Now, let us talk about these permutations in detail.

Posted Date: 3/2/2013 6:06:00 AM | Location : United States

Related Discussions:- Concept of permutation network, Assignment Help, Ask Question on Concept of permutation network, Get Answer, Expert's Help, Concept of permutation network Discussions

Write discussion on Concept of permutation network
Your posts are moderated
Related Questions

What are the key functions of data link layer? Data link layer transfers data in a structured and reliable manner so that the service given by the physical layer is utilized by

Q. What is Manchester? - Utilizes an inversion at the middle of each bit interval for both synchronization and bit representation - Negative-to-positive represents binary 1

State the list of protocols supported by the Intranet The following is the list of protocols supported by the Intranet: ARP: Address resolution Protocol is used to resol

Link State Packet When  a router floods  the network  with information about its  neighbourhood. It is said to  be advertising. The basis of this  advertising is  a short  pack

CONNECTION TO PACKET SWITCHES:  A packet switch many join to devices and to other packet switches. But the speeds are different in both parts. There are typically high-speed j

Illustrate the Bellman-Ford algorithm The Bellman-Ford algorithm uses only on information from its neighbours and knowledge of its link costs, to update it costs and paths. Dij

Q. Focus of Reliability Control? - Implementation of the OSI model puts emphasis on providing a reliable data transfer service while the TCP/IP model treats reliability as an e