Question

Question: 6.16 Refer to Figure 6.14b, which shows an n-cube interconnect topology of order 3 that interconnects 8 nodes. One attractive feature of an n-cube interconnection network topology is its ability to sustain broken links and still provide connectivity.

6.16.1 [10] Develop an equation that computes how many links in the n-cube (where n is the order of the cube) can fail and we can still guarantee an unbroken link will exist to connect any node in the n-cube. 6.16.2 [10] Compare the resiliency to failure of n-cube to a fully-connected interconnection network. Plot a comparison of reliability as a function of the added number of links for the two topologies.

Short answer

6.16.1

For the “n” cube of order$\left(2^n\right)$, the interconnection network can assist N-1 split links, and then it will still also have the guarantee of the existence of a path for all nodes in the required network.

6.16.2

The required plot for comparison:

Step-by-step solution

Define the concept.

6.16.1

For the “n” cube of order_{$\left(2^n\right)$} , the interconnection network can assist N-1 split links, and then it will still also have the guarantee of the existence of a path for all nodes in the required network. Where “n” refers to the order of the given cube. The above equation is able to compute the number of links that can be failed and still after that the unbroken link will have existed which can able to connect all of the nodes of “n cube”.

6.16.2

The straight black line represents the resiliency to failure of the n-cube and the dotted line represents the fully connected interconnection network.

Determine the calculation.

6.16.1

The following equation is able to compute the number of links that can be failed and still after that the unbroken link will have existed which can able to connect all of the nodes of “n cube”.

Where “n” refers to the order of the given cube.

For the “n” cube of order_{$\left(2^n\right)$} , the interconnection network can assist N-1 split links, and then it will still also have the guarantee of the existence of a path for all nodes in the required network.

6.16.2

The following plot represents the comparison.

This difference describes the reliability as a function of the two topologies and mainly the comparison is for the attached number of links.

The required plot for comparison: