Imagine overseeing a network of $n$ interconnected nodes representing different sources of a resource.

Each connection incurs a positive maintenance cost. With a specified budget, you have the opportunity

to establish $k$ resource hubs $($akin to building a hub on a node$).$ The goal is to determine the optimal

set of $k$ nodes for the hubs and the set of connections to retain, minimizing the overall maintenance

cost of the connections. Additionally, the objective is to ensure that each node is connected to at least

one hub through the retained connections. This network is a graph that is connected and undirected

with positive edge weights, assume $|E|=O(|V|).$

Design an algorithm for this and in doing so provide an algorithm description, correctness proof and

runtime anaylsis