In class, we have been discussing trees that span an entire graph. However, it is sometimes useful to split a graph into multiple clusters in cases where we don't need to span the entire graph. Let's say that a college campus has three particular points on campus that are connected to the global Internet. They would like to run fiber across campus so that each building on campus has a path to one of the three global Internet uplinks. Laying fiber is expensive and so they would like to do this by laying the least possible amount of fiber. Devise an algorithm to solve this problem and clearly explain both your algorithm and why it works. What is the worst case runtime of your algorithm (assuming that the campus has N buildings).