A Collision Free Network with Minimal Routing Path for 2<sup>n</sup> Nodes

Abstract

In the present work, a simple but complex network which has collision free communications is created. With the help of the binary n-cube the network is formed. This n-cube network connection is formed by connecting distinct N number of nodes which are expressed as a power of 2. If each node has an address of m bits then there are N=2^m number of nodes in the n-cube network. To find out the predefined routing path for the case of this n-cube network, we can apply deterministic algorithm providing us a collision /deadlock free concept. In calculating the predefined routing path(s), node addresses involved in the path are calculated by using the exclusive OR operation, firstly, upon the two node addresses of source and destination, and then, on the derived node-addresses according to the algorithm stated in section 2. Here, the Exclusive-OR operation is performed simply by using 2-input XOR gate which may be made up of either (i) classical CMOS based material, or (ii) Multiple input threshold logic gate , or (iii) Single electron tunneling Transistor (SET). We are concentrated in the case of CMOS based XOR circuit. In this work, an E-cube Routing on a 6-dimensional hypercube has been designed and constructed. We have tried to find out the node addresses for predefining the deadlock free routing path for any set of “source and destination”. To develop a “Collision free network with minimal Routing”, a number of Exclusive-OR gates are arranged in a pattern discussed in section 3 and the desired circuit is implemented. The implemented circuit can supply the predefined path nodes through which the signal/packets/data can pass. Regarding the experimental input –output values, some truth tables are depicted in substantial places. At the time of applying the algorithm, we have investigated that for 6-dimentional hypercube, the maximum path length are confined to 6, i.e. whenever the source and destination points are provided, then 6-node points are produced. Among these 6-pionts some of them may have identical values. As a result path length should be less than 6. For the network, the time required to travel a path is measured and shown. The net designed and implemented must a be a collision free one, since when a truth table is written, there would not be any pair of nodes identical in a column.