Problem $4(30$ points$)$ Consider a network with $16$ nodes that can be configured in

three different ways:

$(1)$ as a ring,

$(2)$ as a $442$D square grid $($mesh$),$ where each node is connected up to $4$ nearest

neighbors without wrap$-$around,

$(3)$ as a fully connected network.

$2$

Assume that all links provide the same bandwidth, equal to $1$ Gbit$/$s$.$ For each topology,

answer the following questions:

$($a$)(12$ points$)$ What is the total bandwidth?

$($b$)(12$ points$)$ What is the minimum bisection bandwidth? The bisection width of

a network is defined as the minimum number of links that need to be cut to divide the

network into two disconnected parts. The bisection bandwidth is defined as the bandwidth

of the cut links.

$($c$)(6$ points$)$ How many links can fail but still allow us to guarantee that an unbroken

link will exist to connect any node to any other node?