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Problem 3. Suppose a new airline wants to offer connections between $n$ cities (not necessarily nonstop). Market research has determined the number of potential annual customers for nonstop flights between each and every pair of these cities. The airline would like to purchase licenses to offer nonstop flights between exactly $n - 1$ pairs of cities, choosing in such a way as to to connect all $n$ cities while maximizing the sum of potential annual customers for all selected pairs. Describe how to interpret this as a graph problem. What are the vertices, edges, weights, and task? Is the given graph dense or sparse? Describe an algorithm to solve this problem and analyze its runtime.

          Problem 3. Suppose a new airline wants to offer connections between $n$ cities (not necessarily nonstop).
Market research has determined the number of potential annual customers for nonstop flights between each
and every pair of these cities. The airline would like to purchase licenses to offer nonstop flights between
exactly $n - 1$ pairs of cities, choosing in such a way as to to connect all $n$ cities while maximizing the sum
of potential annual customers for all selected pairs.
Describe how to interpret this as a graph problem. What are the vertices, edges, weights, and task? Is
the given graph dense or sparse? Describe an algorithm to solve this problem and analyze its runtime.

Problem 3. Suppose a new airline wants to offer connections between n cities (not necessarily nonstop).
Market research has determined the number of potential annual customers for nonstop flights between each
and every pair of these cities. The airline would like to purchase licenses to offer nonstop flights between
exactly n - 1 pairs of cities, choosing in such a way as to to connect all n cities while maximizing the sum
of potential annual customers for all selected pairs.
Describe how to interpret this as a graph problem. What are the vertices, edges, weights, and task? Is
the given graph dense or sparse? Describe an algorithm to solve this problem and analyze its runtime.

Added by Joaquin S.

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