Ex$.4.$

A company needs reliable internet and phone connectivity across its five New York offices, labeled A$,$ B$,$ C$,$ D$,$ and E for simplicity. To achieve this, they plan to lease dedicated lines between offices from a telecommunications provider. The figure below shows the annual costs $($in thousands of dollars$)$ for each potential connection. The company's objective is to ensure that any office can connect to any other, which means having a path between every pair of offices. To minimize costs,

$($a$)$ Use Kruskal's algorithm to specify the fewest possible connections from the existing options that will keep the network fully connected and at the lowest total cost.

$2$

$($b$)$ Use Prim's algorithm to specify the fewest possible connections from the existing options that will keep the network fully connected and at the lowest total cost.

A company needs reliable internet and phone connectivity across its five New York offices, labeled A$,$ B$,$ C$,$ D$,$ and E for simplicity. To achieve this, they plan to lease dedicated lines between offices from a telecommunications provider. The figure below shows the annual costs $($in thousands of dollars$)$ for each potential connection. The company's objective is to ensure that any office can connect to any other, which means having a path between every pair of offices. To minimize costs,

$($a$)$ Use Kruskal's algorithm to specify the fewest possible connections from the existing options that will keep the network fully connected and at the lowest total cost.

$2$

$($b$)$ Use Prim's algorithm to specify the fewest possible connections from the existing options that will keep the network fully connected and at the lowest total cost.